Zur Veröffentlichung eingereichte Fachberichte

  1. Wavenumber-explicit stablity and convergence analysis of hp-finite element discretizations of Helmholtz problems in piecewise smooth media
    M. Bernkopf, T. Chaumont-Frelet, J.M. Melenk
    arXiv:2209.03601[math.NA]
  2. Exponential convergence of a generalized FEM for heterogeneous reaction-diffusion equations
    C.P. Ma, J.M. Melenk
    arXiv:2209.01957[math.NA]
  3. On interpolation spaces of piecewise polynomials on mixed meshes
    M. Karkulik, J.M. Melenk, A. Rieder
    arXiv:2306.169907[math.NA]
  4. Stability Analysis for Electromagnetic Waveguides. Part 1: Acoustic and Homogeneous Electromagnetic Waveguides
    J.M. Melenk, L. Demkowicz, S. Henneking
    arXiv:2307.04521[math.NA]
  5. Stability Analysis for Electromagnetic Waveguides. Part 2: Nonhomogeneous Waveguides
    L. Demkowicz, J.M. Melenk, J. Badger, S. Henneking
    Oden Institute Report 23-3
  6. Weighted analytic regularity for the integral fractional Laplacian in polyhedra
    Markus Faustmann, Carlo Marcati, Jens Markus Melenk, Christoph Schwab
    arXiv:2307.11679[AP]

Buch

  1. hp-finite element methods for singular perturbations
    Springer LNM 1796 (2002) © Springer-Verlag, 318pp.
    Errata (nicht verfügbar)

Sammelbänder

  1. Direct and Inverse Problems in Wave Propagation and Applications
    (I.G. Graham, U. Langer, J.M. Melenk, M. Sini editors)
    Radon Series on Computational and Applied Mathematics , Vol. 14
    DeGruyter (2013), ISBN: 978-3-11-028228-3
  2. Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2020+1
    (J.M. Melenk, I. Perugia, J. Schöberl, C. Schwab editors)
    Springer Lecture Notes in Computational Sciences, 137
    Springer (2023), ISBN: 978-3-031-20431-9 (hardcover), 978-3-031-20434-0 (softcover) 978-3-031-20432-6 (ebook)

Herausgegebene Journal-Sonderausgabe

  1. Invited Papers from the WAVES 2019 conference
    (M. Kaltenbacher and J.M. Melenk editors) Springer-Nature Partial Differential Equations and Applications (2020)

Buchkapitel

  1. Interpolation and quasi-interpolation in h- and hp-version finite element spaces
    T. Apel, J.M. Melenk
    in: Encyclopedia of Computational Mechanics, second edition, E. Stein, R. de Borst, T. Hughes (eds.), 2017, ISBN: 978-1-119-00379-3, pp. 1-33
    extended preprint version available as ASC Report 39/2015 (PDF)
  2. hp-Version of Finite Element Method
    in: Encyclopedia of Applied and Computational Mathematics, B. Engquist (ed.), 2016, pp. 656-659, ISBN 978-3-540-70528-4 (Print) 978-3-540-70529-1 (Online)
  3. On stability of discretizations of the Helmholtz equation
    S. Esterhazy, J.M. Melenk
    in: Numerical Analysis of Multiscale Problems, I.G. Graham, T.Y. Hou, O. Lakkis, R. Scheichl (Eds.),
    Springer LNCSE 83 (2012), pp. 285-324
    extended version available as ASC Report 01/2011 (PDF) or at arXiv:1105.2112v2 [math.NA]
  4. On Approximation in Meshless Methods
    in: Frontiers in Numerical Analysis, Durham 2004, J. Blowey, A. Craig (eds.), Springer Verlag 2005, pp. 65-141
    available as preprint 11/2004 (PDF)

(Hinweis: In der Regel liegt das Urheberrecht der nachstehenden Dokumente beim Herausgeber - die Links mit der DOI verweisen auf die veröffentlichten Versionen. Die Links zu den früheren technischen Berichten können von den veröffentlichten Endversionen abweichen.)

Begutachtete Artikel

  1. Exponential convergence of hp-FEM for the integral fractional Laplacian in polygons
    M. Faustmann, C. Marcati, J.M. Melenk, C. Schwab
    to appear in SIAM J. Numer. Anal.
    arXiv:2209.11468[math.NA]
  2. Wavenumber-explicit hp-FEM analysis for Maxwell's equations with impedance boundary conditions
    J.M. Melenk, S. Sauter
    to appear in Found. Comp. Math.
    arXiv:2201.02602[math.NA]
  3. Cost-optimal adaptive iterative linearized FEM for semilinear elliptic PDEs
    R. Becker, M. Brunner, M. Innerberger, J.M. Melenk, D. Praetorius
    M2AN 57 (2023), pp. 2193-2225
    arXiv:2211.04123[math.NA]
  4. H-inverses for RBF interpolation
    N. Angleitner, M. Faustmann, J.M. Melenk
    to appear in Adv. Comp. Math.
    arXiv:2109.05763[math.NA]
  5. Exponential meshes and H-matrices
    N. Angleitner, M. Faustmann, J.M. Melenk
    Comput. Math. Appl. 130 (2023) pp. 21-40
    arXiv:2203.09925[math.NA]
  6. hp-FEM for reaction-diffusion equations. II. robust exponential convergence for multiple length scales in corner domains.
    L. Banjai, J.M. Melenk, C. Schwab
    in press in IMA J. Numer. Anal.
    ASC Report 11/2020 (PDF) or at arXiv:2004.10517[math.NA]
  7. An exponentially convergent discretization for space-time fractional parabolic equations using hp-FEM
    J.M. Melenk, A. Rieder
    in press in IMA J. Numer. Anal.
    arXiv:2202.02067[math.NA]
  8. Exponential convergence of hp-FEM for the integral fractional Laplacian in 1D
    B. Bahr, M. Faustmann, C. Marcati, J.M. Melenk, C. Schwab
    in: ICOSAHOM 2020+1 , (Melenk, Perugia, Schöberl, Schwab eds) Springer LCSE 137 pp. 291-306
    arXiv:2204.04113[math.NA]
  9. Exponential convergence of hp-FEM for spectral fractional diffusion in polygons
    L. Banjai, J.M. Melenk, C. Schwab
    Numer. Math. 153 (2023), pp. 1-47
    ASC Report 30/2020 (PDF) or at arXiv:2011.05701[math.NA]
  10. Optimal convergence rates for a first order system least squares method. Part I: homogeneous boundary conditions
    M. Bernkopf, J.M. Melenk
    to appear in M2AN 57 (2023), pp. 107-141
    ASC Report 45/2020 (PDF) or at arXiv:2012.12919[math.NA]
  11. Weighted analytic regularity for the integral fractional Laplacian in polygons
    M. Faustmann, J.M. Melenk, C. Marcati, C. Schwab
    SIAM J. Math. Anal. 54 (2022) pp. 6323-6357
    arXiv:2112.08151[math.AP]
  12. Goal-oriented adaptive finite element method for semilinear elliptic PDEs
    R. Becker, M. Brunner, M. Innerberger, J.M. Melenk, D. Praetorius
    Comput. Math. Appl. 118 (2022), pp. 18--35
    arXiv:2112.06687[math.NA]
  13. Mortar coupling of hp-discontinuous Galerkin and boundary element methods for the Helmholtz equation
    C. Erath, L. Mascotto, J.M. Melenk, I. Perugia, A. Rieder
    J. Sci. Comp. 92:1 (2022), paper nr. 2
    arXiv:2105.06173[math.NA]
  14. H-matrix approximability of inverses of FEM matrices for the time-harmonic Maxwell equation
    M. Faustmann, J.M. Melenk, M. Parvizi
    Adv. Comp. Math. 48 (2022) article nr. 59
    preprint at arXiv:2103.14981[math.NA]
  15. Time domain boundary integral equations and convolution quadrature for scattering by composite media
    A. Rieder, F.-J. Sayas, J.M. Melenk
    Math. Comp. 337 (2022), pp. 2165-2195
    ASC Report 29/2020 (PDF) or at arXiv:2010.14162[math.NA]
  16. Caccioppoli-type estimates and H-Matrix approximations to inverses for FEM-BEM couplings
    M. Faustmann, J.M. Melenk, M. Parvizi
    Numer. Math. 150 (2022), pp. 849-892
    ASC Report 20/2020 (PDF) or at arXiv:2008.11498[math.NA]
  17. Local convergence of the FEM for the integral fractional Laplacian
    M. Faustmann, M. Karkulik, J.M. Melenk
    SIAM J. Numer. Anal. 60 (2022), pp. 1055-1082
    ASC Report 24/2020 (PDF) or at arXiv:2005.14109[math.NA]
  18. Metastable Speeds in the Fractional Allen-Cahn Equation
    F. Achleitner, C. Kuehn, J.M. Melenk, A. Rieder
    Appl. Math. Comp. 408 (2021) Paper nr. 126329
    ASC Report 13/2020 (PDF) or at arXiv:2006.02731[math.DS]
  19. Approximating inverse FEM matrices on non-uniform meshes with H-matrices
    N. Angleitner, M. Faustmann, J.M. Melenk
    Calcolo 58 (2021), Paper nr. 3
    ASC Report 14/2020 (PDF) or at arXiv:2005.04999[math.NA]
  20. Runge-Kutta approximation for \(C_0\)-semigroups in the graph norm with applications to time domain boundary integral equations
    A. Rieder, F.-J., Sayas, J.M. Melenk
    SN PDEs and Applications 1 (2020), Paper nr. 49
    ASC Report 06/2020 (PDF) or at arXiv:2003.01996[math.NA]
  21. On the stability of Scott-Zhang type operators and application to multilevel preconditioning in fractional diffusion
    M. Faustmann, J.M. Melenk, M. Parvizi
    M2AN 55 (2021), pp. 595-625
    ASC Report 03/2020 (PDF) or at arXiv:1912.09160[math.NA]
  22. On superconvergence of Runge-Kutta convolution quadrature for the wave equation
    J.M. Melenk, A. Rieder
    Numer. Math. 147 (2021), p. 157--188
    ASC Report 13/2019 (PDF) or at arXiv:1904.00847[math.NA]
  23. Quasi-optimal convergence rate for an adaptive method for the integral fractional Laplacian
    M. Faustmann, J.M. Melenk, D. Praetorius
    Math. Comp. 90 (2021) pp. 1557-1587
    ASC Report 07/2019 (PDF) or at arXiv:1903.10409[math.NA]
  24. Wavenumber-explicit hp-FEM analysis for Maxwell's equations with transparent boundary conditions
    J.M. Melenk, S.A. Sauter
    Found. Comp. Math. 21 (2021), pp. 125-241
    available at ASC Report 09/2018 (PDF) or at arXiv:1803.01619[math.NA]
  25. \(hp\)-FEM for the fractional heat equation
    J.M. Melenk, A. Rieder
    IMA J. Numer. Anal. 41 (2021), pp. 412-454
    available at ASC Report 12/2019 (PDF) or at arXiv:1901.01767[math.NA]
  26. Wave number-Explicit Analysis for Galerkin Discretizations of Lossy Helmholtz Problems
    J.M. Melenk, S.A. Sauter, C. Torres
    SIAM J. Numer. Anal. 54 (2020), 2119-2143
    available at ASC Report 11/2019 (PDF) or at arXiv:1904.00207[math.NA]
  27. FEM-BEM mortar coupling for the Helmholtz equation in three dimensions
    L. Mascotto, J.M. Melenk, I. Perugia, A. Rieder
    Comp. Math. Appl. 80 (2020), pp. 2351-2378
    available at ASC Report 08/2020 (PDF) or at arXiv:2004.03523[math.NA]
  28. Stable decompositions of \(hp\)-BEM spaces and an optimal Schwarz preconditioner for the hypersingular integral operator in 3D
    M. Karkulik, J.M. Melenk, A. Rieder
    M2AN 54 (2020), pp. 145-180
    available at ASC Report 25/2018 (PDF) or at arXiv:1811.11097[math.NA]
  29. On commuting p-version projection-based interpolation on tetrahedra
    J.M. Melenk, C. Rojik
    Math. comp. 89 (2020), pp. 45-87
    extended version available at ASC Report 05/2018 (PDF) or at arXiv:1802.00197[math.NA]
  30. H-matrix approximability of inverses of discretizations of the fractional Laplacian
    M. Karkulik and J.M. Melenk
    Adv. Comp. Math. 45 (2019), pp. 2893-2919
    ASC Report 25/2018 (PDF) or at arXiv:1808.04274[math.NA]
  31. Analysis of the hp-version of a first order system least squares method for the Helmholtz equation
    M. Bernkopf and J.M. Melenk
    in: Advanced Finite Element Methods with Applications - Selected Papers from the 30th Chemnitz FEM Symposium 2017 (T. Apel, U. Langer, A. Meyer, O. Steinbach eds.), Springer LNCSE 128 (2019), pp. 57-84
    available ASC Report 24/2018 (PDF) or at arXiv:1808.07825[math.NA]
  32. Tensor FEM for spectral fractional diffusion
    L. Banjai, J.M. Melenk, R.H. Nochetto, E. Otárola, A. Salgado, C. Schwab
    Found. Comp. Math. 19 (2019), pp.901-962
    available as ASC Report 13/2017 (PDF) or at arXiv:1707.07367[math.NA]
  33. Local convergence of the BEM on polyhedral domains
    M. Faustmann, J.M. Melenk
    Numer. Math. 140 (2018), pp. 593-637
    available as ASC Report 03/2017 (PDF) or at arXiv:1702.04224[math.NA]
  34. On thin plate spline interpolation
    M. Löhndorf, J.M. Melenk
    ICOSAHOM 2016, Springer LNCSE 119, M. Bittencourt, N. Dumont, J. Hesthaven (eds), pp. 451--466
    available as ASC Report 09/2017 (PDF) or at arXiv:1705.05178[math.NA]
  35. An analysis of a butterfly algorithm
    S. Börm, C. Börst, J.M. Melenk
    Comp. Math. Appl. 74 (2017), pp. 2125-2143
    available at arXiv:1703.01941 or as ASC report 12/2017 (PDF)
  36. Robust exponential convergence of hp-FEM in balanced norms for singularly perturbed reaction-diffusion problems: corner domains
    M. Faustmann, J.M. Melenk
    Comp. Math. Appl. 74 (2017) pp. 1576-1589
    ASC Report 25/2016 (PDF) or at arXiv:1610.09211[math.NA]
  37. Approximation of the high-frequency Helmholtz kernel by nested directional interpolation
    S. Börm, J.M. Melenk
    Numer. Math. 137 (2017), pp. 1-34
    ASC Report 33/2015 (PDF) or at arXiv:1510.07189[math.NA]
  38. Runge-Kutta convolution quadrature and FEM-BEM coupling for the time-dependent linear Schrödinger equation
    J.M. Melenk, A. Rieder
    J. Integral equations and applications 29 (2017), pp. 189-250
    ASC Report 13/2016 (PDF) or at arXiv:1605.07340[math.NA]
  39. Simultaneous quasi-optimal convergence rates in FEM-BEM coupling
    J.M. Melenk, D. Praetorius, B. Wohlmuth
    Math. Methods. Appl. Sci. 40 (2017), pp. 463-485
    also available as ASC Report 13/2014 (PDF) or at arXiv:1404.2744 [math.NA]
  40. An hp-Adaptive Newton-Galerkin Finite Element Procedure for Semilinear Boundary Value Problems
    M. Amrein, J.M. Melenk, T. Wihler
    Math. Methods Appl. Sci. 40 (2017), pp 1973-1985
    available at ASC Report 06/2016 (PDF) or at arXiv:1602.05354[math.NA]
  41. Local inverse estimates for non-local boundary integral operators
    M. Aurada, M. Feischl, T. Führer, M. Karkulik, J.M. Melenk, D. Praetorius
    Math. Comp. 86 (2017), pp. 2651-2686
    available as ASC Report 12/2015 (PDF) or at arXiv:1504.04394 [math.NA]
  42. Existence of H-matrix approximants to the inverse of BEM matrices: the hyper-singular integral operator
    M. Faustmann, J.M. Melenk, D. Praetorius
    IMA J. Numer. Anal. 37 (2017) pp. 1211-1244
    available as ASC Report 08/2015 (PDF) or at arXiv:1503.01943[math.NA]
  43. Existence of H-matrix approximants to the inverses of BEM matrices: the simple-layer operator
    M. Faustmann, J.M. Melenk, D. Praetorius
    Math. Comp. 85 (2016), pp 119-152
    also available as ASC Report 37/2013 (PDF) and arXiv:1311.5028 [math.NA]
  44. Robust exponential convergence of hp-FEM in balanced norms for singularly perturbed reaction-diffusion equations
    J.M. Melenk, C. Xenophontos
    Calcolo 53 (2016), pp. 105-132
    available as ASC Report 24/2014 (PDF) or at arXiv:1408.3328[math.NA]
  45. Local high-order regularization and applications to hp-methods
    M. Karkulik, J.M. Melenk
    Comp. Math. Appl. 70 (2015), pp. 1606-1639
    preprint version available as
    ASC Report 38/2014 (PDF) or at arXiv:1411.5209[math.NA]
  46. Optimal additive Schwarz methods for the hp-BEM: the hypersingular integral operator in 3D on locally refined meshes
    T. Führer, J.M. Melenk, D. Praetorius, A. Rieder
    Comp. Math. Appl. 70 (2015), pp. 1583-1605
    available as ASC Report 41/2014 (PDF) or at arXiv:1412.2024[math.NA]
  47. On optimal L^2 and surface flux convergence in FEM
    T. Horger, J.M. Melenk, B. Wohlmuth
    CVS 16 (2013), pp. 231-246
    ASC Report 02/2015 (PDF) or at arXiv:1501.03003 [math.NA]
  48. When is the error in the h-BEM for solving the Helmholtz equation bounded independently of k?
    I.G. Graham, M. Löhndorf, J.M. Melenk, E.A. Spence
    BIT 55 (2015), pp. 171-214
    ASC Report 28/2013 (PDF)
  49. H-matrix approximability of the inverse of FEM matrices
    M. Faustmann, J.M. Melenk, D. Praetorius
    Numer. Math. 131 (2015), pp. 615-642
    available as ASC Report 20/2013 (PDF) and arXiv:1308.0499 [math.NA]
  50. FEM-BEM coupling for the large-body limit in micromagnetics
    M. Aurada, J.M. Melenk, D. Praetorius
    J. Comp. Math. 281 (2015), pp. 10-31
    also available as ASC Report 4/2013 (PDF)
  51. Quasi-optimal convergence rates for adaptive BEMs with data approximation. Part II: hyper-singular integral equation
    M. Feischl, T. Führer, M. Karkulik, J.M. Melenk, D. Praetorius
    Electron. Trans. Numer. Anal 44 (2015), pp. 153-176
    also available as ASC Report 30/2013 (PDF)
  52. A scalable numerical approach for the Steady-State Ab-Initio Laser Theory
    S. Esterhazy, D. Liu, M. Liertzer, A. Cerjan, L. Ge, K.G. Makris, A.D. Stone, J.M. Melenk, S.G. Johnson, S. Rotter
    Phys. Rev. A 90 023816 (2014)
    also available as ASC Report 40/2013 (PDF) and arXiv:1312.2488 [physics.optics]
  53. On the stability of the boundary trace of the polynomial L^2 projection on triangles and tetrahedra
    J.M. Melenk, T. Wurzer
    Comp. Math. Appl. 67 (2014), pp. 944-965
    also available as extended versions (with slightly different title) at ASC Report 25/2012 (PDF) or arXiv:1302.7189 [math.NA]
  54. An analysis of discretizations of the Helmholtz equation in L^2 and in negative norms
    S. Esterhazy, J.M. Melenk
    Comp. Math. Appl. 67 (2014), pp. 830-853
    extended version available as ASC Report 31/2012 (PDF) or as corrected version (PS)
  55. Quasi-optimal convergence rates for adaptive BEMs with data approximation. Part I: weakly singular integral equations
    M. Feischl, T. Führer, M. Karkulik, J.M. Melenk, D. Praetorius
    Calcolo 51 (2014), pp. 531--562
    available as ASC Report 24/2013 (PDF)
  56. Mixed conforming elements for the large-body limit in micromagnetics
    M. Aurada, J.M. Melenk, D. Praetorius
    M3AS 24 (2014), pp. 113--144
    available (with a different title) as ASC Report 42/2011 (PDF)
  57. Quasi-optimal a priori estimates for fluxes in mixed finite element methods and applications to the Stokes--Darcy coupling
    J.M. Melenk, H. Rezaijafari, B. Wohlmuth
    IMA J. Numer. Anal. 34 (2014), pp. 1-27
    available as ASC Report 05/2012 (PDF)
  58. General DG-Methods for Highly Indefinite Helmholtz Problems
    J.M. Melenk, A. Parsania, S. Sauter
    J. Sci. Comp. 57 (2013), pp. 536-581
    available as corrected version (PS) of ASC Report 06/2012 (PDF) (with slightly different title)
  59. Symmetry-free, p-robust equilibrated error indication for the hp-version of the FEM in almost incompressible linear elasticity
    P. Dörsek, J.M. Melenk
    CMAM 13 (2013), pp 291--304
    available as ASC Report 46/2012 (PDF)
  60. A numerical study of averaging error indicators in p-FEM
    P. Dörsek, J.M. Melenk
    in: Spectral and High Order Methods for Partial Differential Equations - ICOSAHOM 2012,
    Azaiez, M., El Fekih, H., Hesthaven, J. (eds), LCSE 95, Springer, 2014, pp. 227-236
    available as ASC Report 45/2012 (PDF)
  61. Quasi-optimal convergence rate for an adaptive boundary element method
    M. Feischl, M. Karkulik, J.M. Melenk, D. Praetorius
    SIAM J. Numer. Anal. 51 (2013), pp. 1327--1348
    available as ASC Report 28/2011 (PDF)
  62. A high frequency hp-boundary element method for scattering by convex polygons
    D.P. Hewett, S. Langdon, J.M. Melenk
    SIAM J. Numer. Anal. 51 (2013), pp. 629--653
    available as ASC Report 40/2011 (PDF)
  63. Analytic regularity for a singularly perturbed system of reaction-diffusion equations with multiple scales: a roadmap
    J.M. Melenk, C. Xenophontos, L. Oberbroeckling
    Adv. Comp. Math. 39 (2013), pp. 367-394
    available as extended version (with slightly different title): as ASC Report 29/2011 (PDF) and at arXiv:1108.2002 [math.NA]
  64. Robust exponential convergence of hp-FEM for singularly perturbed reaction-diffusion systems with multiple scales
    J.M. Melenk, C. Xenophontos, L. Oberbroeckling
    IMA J. Numer. Anal. 33 (2013), pp. 609--628
    available as revised version (PS) of ASC Report 31/2011 (PDF)
  65. Classical FEM-BEM coupling methods: nonlinearities, well-posedness, and adaptivity
    M. Aurada, M. Feischl, T. Führer, M. Karkulik, J.M. Melenk, D. Praetorius
    Comp. Mech. 51 (2013), pp. 399--419
    available as ASC Report 08/2012 (PDF) or at arXiv:1211.4225 [math.NA]
  66. Quasi-optimal approximation of surface based Lagrange multipliers in finite element methods
    J.M. Melenk, B. Wohlmuth
    SIAM J. Numer. Anal. 50 (2012), pp. 2064--2087
    available as ASC Report 13/2011 (PDF) and as corrected version (PS)
  67. Mapping properties of combined field Helmholtz boundary integral operators
    SIAM J. Math. Anal. 44 (2012), pp. 2599--2636
    corrected version (PS) of ASC Report 01/2010 (PDF)
  68. Numerical quadratic energy minimization bound to convex constraints in thin-film micromagnetics
    S. Ferraz-Leite, J.M. Melenk, D. Praetorius
    Numer. Math. 122 (2012), pp. 101--131
    available as ASC Report 32/2011 (PDF)
  69. Wavenumber-explicit hp-BEM for high frequency scattering
    M. Löhndorf, J.M. Melenk
    SIAM J. Numer. Anal. 49 (2011), pp. 2340--2363
    available as corrected version (PS) of ASC Report 02/2010 (PDF)
  70. Wavenumber explicit convergence analysis for Galerkin discretizations of the Helmholtz equation
    J.M. Melenk, S. Sauter
    SIAM J. Numer. Anal. 49 (2011), pp. 1210--1243
    extended version available as corrected version (PS) of ASC Report 31/2009 (PDF)
  71. Runge-Kutta convolution quadrature for operators arising in wave propagation
    L. Banjai, C. Lubich, J.M. Melenk
    Numer. Math., 119 (2011), pp. 1-20
    available as ASC Report 24/2010 (PDF)
  72. Adaptive hp-FEM for the contact problem with Tresca friction in linear elasticity: the primal-dual formulation and a posteriori error estimation
    P. Dörsek, J.M. Melenk
    Appl. Numer. Math. 60 (2010), pp. 689--704
    extended version available as ASC Report 37/2009 (PDF)
  73. hp-FEM for the contact problem with Tresca friction in linear elasticity: the primal formulation
    P. Dörsek, J.M. Melenk
    in: Spectral and high order methods for PDEs, J. Hesthaven, E. Rønquist eds, pp. 1-17, LNCSE 76, Springer Verlag (2011)
    extended version available as ASC Report 36/2009 (PDF)
  74. Convergence Analysis for Finite Element Discretizations of the Helmholtz equation with Dirichlet-to-Neumann boundary conditions
    J.M. Melenk, S. Sauter
    Math. Comp. 79 (2010), pp. 1871--1914
    available as revised version (PDF) of ASC Report 15/2008 (PDF)
  75. Optimal Convergence of Higher Order Finite Element Methods for Elliptic Interface Problems
    Jingzhi Li, J.M. Melenk, Barbara Wohlmuth, Jun Zou
    Appl. Numer. Math. , 60 (2010), pp. 19--37
    available as revised version (PS) of ASC Report 13/2008 (PDF)
  76. On the suboptimality of the p-version interior penalty discontinuous Galerkin method
    E. Georgoulis, E. Hall, J.M. Melenk
    J. Sci. Comp. 42 (2010), pp. 54-67
    available as ASC Report 03/2009 (PDF)
  77. On the convergence of Filon quadrature
    J. Comput. Appl. Math. , 234 (2010), pp. 1692--1701
    extended version available as ASC Report 08/2008 (PDF)
  78. p-FEM quadrature error analysis on tetrahedra
    T. Eibner, J.M. Melenk, in: Proceedings of DD17, Langer, Discacciati, Keyes, Widlund, Zulehner (eds.), Springer LNSCE vol. 60 (2008), pp. 493-500 (ISSN 1439-7358)
    available as ASC Report 23/2007 (PDF)
  79. Multilevel preconditioning for the boundary concentrated hp-FEM
    T. Eibner, J.M. Melenk
    Comp. Meth. Mech. Eng. 196 (2007), pp. 3713-3725
    available as Preprint 05-13 (PS) of the SFB 393
  80. Additive Schwarz preconditioning for p-version triangular and tetrahedral finite elements
    J. Schöberl, J.M. Melenk, C. Pechstein, S. Zaglmayr,
    IMA J. Numer. Anal. 28 (2008), pp. 1-24
    this article was among the top 5 downloads in 2008
    available as Preprint 11/2005 of the Radon institute
  81. Fast algorithms for setting up the stiffness matrix in hp-FEM: a comparison
    T. Eibner, J.M. Melenk
    preprint version (PS)
    in: Computer Mathematics and its Applications-Advances and Developments (1994-2005), Elias A. Lipitakis (Ed.), LEA Publ., Athens, Greece, pp. 575-596, ISBN: 960-87275-9-6
  82. An adaptive strategy for hp-FEM based on testing for analyticity
    T. Eibner and J.M. Melenk
    Comp. Mech. 39 (2007), pp. 575-595
    preprint version (PDF)
  83. A local error analysis of the boundary concentrated FEM
    T. Eibner and J.M. Melenk
    IMA J. Numer. Anal. 26 (2006), pp.752-778
    preprint version (PS)
  84. hp-interpolation of non-smooth functions
    SIAM J. Numer. Anal. 43 (2005), pp. 127-155
    extended version is available as
    Preprint NI03050 of the Isaac Newton Institute for Mathematical Sciences
  85. Approximation of integral operators by variable-order interpolation
    S. Börm, M. Löhndorf, J.M. Melenk
    Numer. Math. 99 (2005), pp. 605-643
    preprint version
  86. Mortar methods with curved interfaces
    B. Flemisch, J.M. Melenk, B. Wohlmuth,
    Appl. Numer. Math. 54 (2005), pp. 339-361
    preprint version
  87. Two-scale regularity for homogenization problems with non-smooth fine scale geometry
    A.-M. Matache & J.M. Melenk
    M3AS, 13 (2003), pp. 1053-1080
    available as Preprint 63 (PS) of the DFG priority program "multiscale problems"
  88. Boundary concentrated FEM
    B.I. Khoromskij & J.M. Melenk,
    SIAM J. Numer. Anal. 41 (2003), pp. 1-36
    preprint version
  89. An efficient direct solver for the boundary concentrated FEM in 2D
    B.I. Khoromskij & J.M. Melenk,
    Computing 69 (2002), pp. 91-117
    preprint version
  90. On condition numbers in hp-FEM with Gauß-Lobatto based shape functions
    J. Comput. Appl. Math. , 139 (2002), pp. 21-48
    preprint version (PS.GZ)
  91. On residual-based aposteriori error estimation in hp -FEM
    J.M. Melenk & B. Wohlmuth,
    Advances in Comput. Math. , 15 (2001), pp. 311-331
    preprint version (PS.GZ)
  92. Approximation orders for natural splines in arbitrary dimensions
    J.M. Melenk & T. Gutzmer,
    Math. Comput. 70 (2001), pp. 699-703
    preprint version (PS.GZ)
  93. Fully discrete hp finite elements: fast quadrature
    J.M. Melenk, K. Gerdes, & C. Schwab,
    Comput. Meths. Appl. Mech. Engrg. 190 (2001), pp. 4339-4364
    preprint version
  94. The hp-version of the Streamline Diffusion Finite Element Method in two dimensions,
    K. Gerdes, J.M. Melenk, D. Schötzau, & C. Schwab,
    M3AS 11 (2001), pp. 301-337
    abstract and paper
  95. Spectral Galerkin discretizations for hydrodynamic stability problems
    J.M. Melenk, N.P. Kirchner, & C. Schwab,
    Computing 65 (2000), p. 97-118
    abstract and paper
  96. On n-widths for elliptic problems
    J. Math. Anal. Appl. 247 (2000), p. 272-289
    preprint version (PS.GZ)
  97. The hp-Streamline Diffusion Method for Convection Dominated Problems in One Space Dimension
    J.M. Melenk & C. Schwab,
    East-West J. Numer. Math. 7 (1999), 31-60
    abstract and paper
  98. Operator adapted spectral element methods. I: harmonic and generalized harmonic polynomials
    Numer. Math. 84 (1999), p. 35-69
    preprint version
  99. An hp FEM for convection-diffusion problems in one dimension
    J.M. Melenk & C. Schwab,
    IMA J. Numer. Anal. 19 (1999), 425-453
    abstract and paper
  100. Analytic regularity for a singularly perturbed problem
    J.M. Melenk & C. Schwab,
    SIAM J. Math. Anal., 30 (1999), 379-400
    preprint version
  101. hp-FEM for Reaction-Diffusion Equations. I: Robust Exponential Convergence
    J.M. Melenk & C. Schwab,
    SIAM J. Numer. Anal., 35 (1998), 1520-1557
    preprint version
  102. On the Robust Exponential Convergence of hp-FEMs for Problems with Boundary Layers
    IMA J. Numer. Anal., 17 (1997), 577-601
    abstract and paper
  103. Approximation with harmonic and generalized harmonic polynomials in the partition of unity method
    J.M. Melenk & I. Babuska
    Comput. Assist. Mech. Eng. Sci. 4 (1997), 607-632
    Load Postscript (PS.GZ)
  104. The Partition of Unity Method
    I. Babuska & J.M. Melenk,
    Int. J. Numer. Meths. Eng., 40 (1997), 727-758
    preprint version (PS.GZ)
  105. The Partition of Unity Finite Element Method: Basic Theory and Applications
    J.M. Melenk & I. Babuska,
    Comput. Meths. Appl. Mech. Engrg.,139 (1996), 289-314
    abstract and paper
  106. Finite Element Method for Solving Problems with Singular Solutions
    I. Babuska, B. Andersson, B. Guo, J.M. Melenk, & H.-S. Oh,
    J. Comput. Appl. Math. , 74 (1996),51-70
    preprint version (PS.GZ)
  107. Functions with time- and frequency-gaps
    J.M. Melenk & G. Zimmermann,
    J. Fourier Anal. Appl. , 2 (6), 1996
    preprint version (PS.GZ)

Ausgewählte Beiträge zu Proceedings

  1. Optimally truncated WKB approximation for the highly oscillatory stationary 1D Schrödinger equation
    J. Körner, A. Arnold,C. Klein, J.M. Melenk
    extended abstract for ICNAAM 2023
    arXiv 2310.00955
  2. hp-FEM for the spectral fractional Laplacian
    L. Banjai, J.M. Melenk, C. Schwab
    Oberwolfach Report , 2019/40
  3. hp-FEM and hp-DGFEM for Helmholtz problems
    S. Esterhazy, J.M. Melenk, A. Parsania, S. Sauter
    Oberwolfach Report , 2013/03
  4. H-matrix approximability of the inverses of first kind BEM matrices
    M. Faustmann, J.M. Melenk, and D. Praetorius
    Oberwolfach Report , 2012/55
  5. A new proof for existence of H-matrix approximants to the inverse of FEM matrices: the Dirichlet problem for the Laplacian.
    M. Faustmann, J.M. Melenk, and D. Praetorius
    in: Spectral and High Order Methods for Partial Differential Equations - ICOSAHOM 2012,
    Azaiez, M., El Fekih, H., Hesthaven, J. (eds), LCSE 95, Springer, 2014, pp. 249-259
    ASC Report 51/2012 (PDF)
  6. novel inverse estimates for non-local operators
    M. Feischl, Tührer, M. Karkulik, J. Melenk, D. Praetorius:
    extended abstract for IABEM 2012
    ASC Report 49/2012 (PDF)
  7. FEM-BEM Couplings without Stabilization
    M. Feischl, T. Führer, M. Karkulik, J. Melenk, D. Praetorius:
    extended abstract for IABEM 2012
    ASC Report 47/2012 (PDF)
  8. Mixed Conforming Elements for the Large-Body Limit in Micromagnetics
    M. Aurada, J.M. Melenk, D. Praetorius
    proceedings of MathMod 2009
    ASC Report 49/2009 (PDF)
  9. Reduced Model in Thin-Film Micromagnetics
    S. Ferraz-Leite, J.M. Melenk, D. Praetorius
    proceedings of MathMod 2009
    ASC Report 02/2009 (PDF)
  10. Residual a-posteriori error estimates in BEM: Convergence of h-adaptive algorithms
    M. Feischl, M. Karkulik, J. Melenk, D. Praetorius:
    extended abstract for IABEM 2009

Unveröffentlichte Fachberichte und ausgewählte BA- und MA-Arbeiten

  1. mapping properties of Helmholtz boundary integral operators and their application to the hp-BEM
    M. Löhndorf and J.M. Melenk
    ASC Report 34/2009 (PDF)
  2. stability of the trace of the polynomial L2 projection on triangles
    Bachelor thesis of T. Wurzer
    ASC Report 36/2010 (PDF)
    an extended version that includes the 3D case is at arXiv:1302.7189 [math.NA]
  3. Analytic regularity for a singularly perturbed system of reaction-diffusion equations with multiple scales: proofs
    J.M. Melenk, C. Xenophontos, L. Oberbroeckling
    ASC Report 29/2011 (PDF) and at arXiv:1108.2002 [math.NA]
  4. Inverse estimates for elliptic integral operators and their application to the adaptive coupling of FEM and BEM
    M. Aurada, M. Feischl, T. Führer, M. Karkulik, J.M. Melenk, D. Praetorius
    ASC Report 07/2012 (PDF) or at arXiv:1211.4360 [math.NA]
  5. A Posteriori Error Analysis of hp-FEM for singularly perturbed problems reaction-diffusion equations
    J.M. Melenk, T. Wihler
    ASC Report 25/2014 (PDF) or at arXiv:1408.6037[math.NA]

Skripten

  • A first course in Numerical Analysis (250pp)
    bitte fragen Sie nach einer Kopie
  • FEM
    bitte fragen Sie nach einer Kopie
  • Numerical methods for ODEs (100pp)
    bitte fragen Sie nach einer Kopie