Humboldt-Universität zu Berlin
Department of Mathematics
Numerical Analysis



least-squares finite element methods, discontinuous Petrov-Galerkin finite element methods, adaptive mesh refinement, Stokes equations, elasticity, nonlinear problems


  1. C. Carstensen, P. Bringmann, F. Hellwig, and P. Wriggers. Nonlinear discontinuous Petrov-Galerkin methods. Numer. Math. 139(3): 529-561, 2018. DOI: 10.1007/s00211-018-0947-5.
    Preprint available at arXiv.org: 1710.00529 [math.NA].
  2. P. Bringmann, C. Carstensen, and 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.
  3. P. Bringmann and 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.
  4. C. Carstensen, E.-J. Park, and P. Bringmann. Convergence of natural adaptive least squares finite element methods. Numer. Math. 136(4): 1097-1115, 2017. DOI: 10.1007/s00211-017-0866-x.
  5. P. Bringmann and C. Carstensen. An adaptive least-squares FEM for the Stokes equations with optimal convergence rates. Numer. Math. 135(2): 459-492, 2017. DOI: 10.1007/s00211-016-0806-1.
  6. P. Bringmann, C. Carstensen, D. Gallistl, F. Hellwig, D. Peterseim, S. Puttkammer, H. Rabus, and J. Storn. Towards adaptive discontinuous Petrov-Galerkin methods. PAMM. Proc. Appl. Math. Mech. 16(1): 741-742, 2016. DOI: 10.1002/pamm.201610359.
  7. P. Bringmann, C. Carstensen, and C. Merdon. Guaranteed velocity error control for the pseudostress approximation of the Stokes equations. Numer. Methods Partial Differential Equations 32(5): 1411-1432, 2016. DOI: 10.1002/num.22056.

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