• Numerische Lösung von PDEs

  • Least-Squares-Finite-Elemente-Methoden

  • adaptive Netzverfeinerung

  • iterative Linearisierungsverfahren

  • diskontinuierliche Petrov-Galerkin-Methoden

  • nichtkonforme Methoden

  • Anwendungen in der Mechanik

  1. P. Bringmann, A. Miraçi, D. Praetorius. Iterative solvers in adaptive FEM. Adaptivity yields quasi-optimal computational runtime. In: F. Chouly, S. Bordas, R. Becker und P. Omnes (Hrsg.), Error Control, Adaptive Discretizations, and Applications. Advances in Applied Mechanics (AAMS), vol. 58. Elsevier, 2024. [doi:10.1016/bs.aams.2024.08.002] | [arxiv:2404.07126]
  2. P. Bringmann. Review and computational comparison of adaptive least-squares finite element schemes, Comput. Math. Appl. 172: 1–15­, 2024. [doi:10.1016/j.camwa.2024.07.022]
  3. P. Bringmann, M. Brunner, D. Praetorius, J. Streitberger. Optimal complexity of goal-oriented adaptive FEM for nonsymmetric linear elliptic PDEs, J. Numer. Math., online veröffentlicht, 2024. [doi:10.1515/jnma-2023-0150]
  4. P. Bringmann, J. W. Ketteler, M. Schedensack. Discrete Helmholtz decompositions of piecewise constant and piecewise affine vector and tensor fields, Found. Comput. Math., online veröffentlicht, 2024. [doi:10.1007/s10208-024-09642-1]
  5. P. Bringmann, C. Carstensen, J. Streitberger. Local parameter selection in the C0 interior penalty method for the biharmonic equation. J. Numer. Math. 32(3): 257–273, 2024. [doi:10.1515/jnma-2023-0028]
  6. P. Bringmann. How to prove optimal convergence rates for adaptive least-squares finite element methods. J. Numer. Math. 31(1): 43–58, 2023. [doi:10.1515/jnma-2021-0116]
  7. P. Bringmann, C. Carstensen, N. T. Tran. Adaptive least-squares, discontinuous Petrov-Galerkin, and hybrid high-order methods. In: J. Schröder, P. Wriggers (Hrsg.) Non-standard Discretisation Methods in Solid Mechanics. Lecture Notes in Applied and Computational Mechanics, Vol. 98. Springer, Cham, 2022. [doi:10.1007/978-3-030-92672-4_5]
  8. P. Bringmann, C. Carstensen, G. Starke. An adaptive least-squares FEM for linear elasticity with optimal convergence rates. SIAM J. Numer. Anal. 56(1): 428–447, 2018. [doi:10.1137/16M1083797]
  9. C. Carstensen, P. Bringmann, F. Hellwig, P. Wriggers. Nonlinear discontinuous Petrov-Galerkin methods. Numer. Math. 139: 529–561, 2018. [doi:10.1007/s00211-018-0947-5]
  10. P. Bringmann, C. Carstensen. h-adaptive least-squares finite element methods for the 2D Stokes equations of any order with optimal convergence rates. Comput. Math. Appl. 74(8): 1923–1939, 2017. [doi:10.1016/j.camwa.2017.02.019]
  11. P. Bringmann, C. Carstensen. An adaptive least-squares FEM for the Stokes equations with optimal convergence rates. Numer. Math. 135: 459–492, 2017. [doi:10.1007/s00211-016-0806-1]
  12. C. Carstensen, E. J. Park, P. Bringmann. Convergence of natural adaptive least squares FEMs. Numer. Math. 136: 1097–1115, 2017. [doi:10.1007/s00211-017-0866-x]
  13. P. Bringmann, C. Carstensen, C. Merdon. Guaranteed velocity error control for the pseudo-stress approximation of the Stokes equations. Numer. Methods Partial Differential Eqs 32: 1411-1432, 2016. [doi:10.1002/num.22056]
  14. P. Bringmann, C. Carstensen, D. Gallistl, F. Hellwig, D. Peterseim, S. Puttkammer, H. Rabus, J. Storn. Towards adaptive discontinuous Petrov-Galerkin methods. Proc. Appl. Math. Mech. 16: 741-742, 2016. [doi:10.1002/pamm.201610359]

  1. P. Bringmann, M. Feischl, A. Miraçi, D. Praetorius, J. Streitberger. On full linear convergence and optimal complexity of adaptive FEM with inexact solver, 2023. [arxiv:2311.15738]
  2. P. Bringmann. Scaling-robust built-in a posteriori error estimation for discontinuous least-squares finite element methods, 2023, [arxiv:2310.19930]

  1. P. Bringmann, M. Feischl, A. Miraçi, D. Praetorius, J. Streitberger. On full linear convergence and optimal complexity of adaptive FEM with inexact solver. Chemnitz Finite Element Symposium 2024, Deutschland. [Folien]