Publications
- Work indexed by Mathematical Review
- Work indexed by Zentralblatt
- Preprints on ArXiv
- Google Scholar profile
- Submitted articles
- Refereed articles
- Books and book chapters
- Unpublished technical reports and selected theses
Technical reports submitted for publication
- 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] - Exponential convergence of a generalized FEM for heterogeneous reaction-diffusion equations
C.P. Ma, J.M. Melenk
arXiv:2209.01957[math.NA] - On interpolation spaces of piecewise polynomials on mixed meshes
M. Karkulik, J.M. Melenk, A. Rieder
arXiv:2306.169907[math.NA] - Stability Analysis for Electromagnetic Waveguides. Part 1: Acoustic and Homogeneous Electromagnetic Waveguides
J.M. Melenk, L. Demkowicz, S. Henneking
arXiv:2307.04521[math.NA] - Stability Analysis for Electromagnetic Waveguides. Part 2: Nonhomogeneous Waveguides
L. Demkowicz, J.M. Melenk, J. Badger, S. Henneking
Oden Institute Report 23-3 - Weighted analytic regularity for the integral fractional Laplacian in polyhedra
Markus Faustmann, Carlo Marcati, Jens Markus Melenk, Christoph Schwab
arXiv:2307.11679[AP]
Book
- hp-finite element methods for singular perturbations
Springer LNM 1796 (2002) © Springer-Verlag, 318pp.
Errata (nicht verfügbar)
Edited Books
- 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 - 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)
Edited Special Journal Issue
- Invited Papers from the WAVES 2019 conference
(M. Kaltenbacher and J.M. Melenk editors) Springer-Nature Partial Differential Equations and Applications (2020)
Book Chapters
- 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) - 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) - 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] - 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)
(Note: usually the copyright of the papers below is with the publisher - the links using the DOI point to the published versions. Links to the earlier technical reports may differ from the final published versions.)
Refereed articles
- 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] - 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] - 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] - H-inverses for RBF interpolation
N. Angleitner, M. Faustmann, J.M. Melenk
to appear in Adv. Comp. Math.
arXiv:2109.05763[math.NA] - 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] - 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] - 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] - 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] - 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] - 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] - 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] - 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] - 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] - 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] - 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] - 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] - 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] - 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] - 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] - 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] - 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] - 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] - 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] - 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] - \(hp\)-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] - 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] - 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] - 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] - 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] - 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] - 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] - 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] - 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] - 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] - 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) - 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] - 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] - 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] - 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] - 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] - 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] - 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] - 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] - 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] - 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] - 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] - 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] - 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) - 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] - 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) - 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) - 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] - 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] - 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) - 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) - 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) - 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) - 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) - 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) - 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) - 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) - 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) - 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] - 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) - 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] - 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) - 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) - 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) - 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) - 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) - 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) - 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) - 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) - 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) - 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) - 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) - On the convergence of Filon quadrature
J. Comput. Appl. Math. , 234 (2010), pp. 1692--1701
extended version available as ASC Report 08/2008 (PDF) - 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) - 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 - 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 - 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 - 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) - 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) - 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 - Approximation of integral operators by variable-order interpolation
S. Börm, M. Löhndorf, J.M. Melenk
Numer. Math. 99 (2005), pp. 605-643
preprint version - Mortar methods with curved interfaces
B. Flemisch, J.M. Melenk, B. Wohlmuth,
Appl. Numer. Math. 54 (2005), pp. 339-361
preprint version - 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" - Boundary concentrated FEM
B.I. Khoromskij & J.M. Melenk,
SIAM J. Numer. Anal. 41 (2003), pp. 1-36
preprint version - 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 - 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) - 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) - Approximation orders for natural splines in arbitrary dimensions
J.M. Melenk & T. Gutzmer,
Math. Comput. 70 (2001), pp. 699-703
preprint version (PS.GZ) - 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 - 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 - Spectral Galerkin discretizations for hydrodynamic stability problems
J.M. Melenk, N.P. Kirchner, & C. Schwab,
Computing 65 (2000), p. 97-118
abstract and paper - On n-widths for elliptic problems
J. Math. Anal. Appl. 247 (2000), p. 272-289
preprint version (PS.GZ) - 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 - Operator adapted spectral element methods. I: harmonic and generalized harmonic polynomials
Numer. Math. 84 (1999), p. 35-69
preprint version - 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 - Analytic regularity for a singularly perturbed problem
J.M. Melenk & C. Schwab,
SIAM J. Math. Anal., 30 (1999), 379-400
preprint version - 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 - On the Robust Exponential Convergence of hp-FEMs for Problems with Boundary Layers
IMA J. Numer. Anal., 17 (1997), 577-601
abstract and paper - 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) - The Partition of Unity Method
I. Babuska & J.M. Melenk,
Int. J. Numer. Meths. Eng., 40 (1997), 727-758
preprint version (PS.GZ) - 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 - 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) - Functions with time- and frequency-gaps
J.M. Melenk & G. Zimmermann,
J. Fourier Anal. Appl. , 2 (6), 1996
preprint version (PS.GZ)
Theses
- hp-Finite Element Methods for Singular Perturbations (PS.GZ)
Habilitation Thesis 2000 - On Generalized Finite Element Methods (PS.GZ)
PhD Thesis 1995 - Finite element methods with harmonic shape functions for solving Laplace's equation (PS.GZ)
MA Thesis 1992
Selected Proceedings Contributions
- 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 - hp-FEM for the spectral fractional Laplacian
L. Banjai, J.M. Melenk, C. Schwab
Oberwolfach Report , 2019/40 - hp-FEM and hp-DGFEM for Helmholtz problems
S. Esterhazy, J.M. Melenk, A. Parsania, S. Sauter
Oberwolfach Report , 2013/03 - H-matrix approximability of the inverses of first kind BEM matrices
M. Faustmann, J.M. Melenk, and D. Praetorius
Oberwolfach Report , 2012/55 - 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) - 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) - 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) - 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) - Reduced Model in Thin-Film Micromagnetics
S. Ferraz-Leite, J.M. Melenk, D. Praetorius
proceedings of MathMod 2009
ASC Report 02/2009 (PDF) - 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
Unpublished Technical Reports and Selected BA and MA Theses
- 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) - 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] - 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] - 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] - 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]
Class Notes
- A first course in Numerical Analysis (250pp, in German)
please ask for a copy - FEM
please ask for a copy - Numerical methods for ODEs (100pp, in German)
please ask for a copy