5 citations · 12 across the 9 of their papers we have counts for
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Optimal complexity of adaptive FEM for second-order linear elliptic PDEs driven by non-residual estimators, Part I: Symmetric PDEs
Philipp Bringmann, Aleksandar Dadic, Dario Ferloni +3
We consider adaptive finite element methods for symmetric second-order linear elliptic PDEs, where the adaptive algorithm steers the local mesh refinement as well as an iterative a…
Unconditional full linear convergence and quasi-optimal complexity of smoothed adaptive finite element methods
Philipp Bringmann, Christoph Lietz, Dirk Praetorius
We present the first rigorous convergence analysis of the smoothed adaptive finite element method (S-AFEM) proposed in [Mulita, Giani, Heltai: SIAM J. Sci. Comput. 43, 2021]. S-AFE…
Newton's method in adaptive iteratively linearized FEM
Philipp Bringmann, Maximilian Brunner, Dirk Praetorius
This paper concerns the inclusion of Newton's method into an adaptive finite element method (FEM) for the solution of nonlinear partial differential equations (PDEs). It features a…
Global convergence of adaptive least-squares finite element methods for nonlinear PDEs
Philipp Bringmann, Dirk Praetorius
The Zarantonello fixed-point iteration is an established linearization scheme for quasilinear PDEs with strongly monotone and Lipschitz continuous nonlinearity in Hilbert spaces. T…
Iterative solvers in adaptive FEM
Philipp Bringmann, Ani Miraçi, Dirk Praetorius
This chapter provides an overview of state-of-the-art adaptive finite element methods (AFEMs) for the numerical solution of second-order elliptic partial differential equations (PD…
Optimal complexity of goal-oriented adaptive FEM for nonsymmetric linear elliptic PDEs
Philipp Bringmann, Maximilian Brunner, Dirk Praetorius +1
We analyze a goal-oriented adaptive algorithm that aims to efficiently compute the quantity of interest with a linear goal functional and the solution to…
On full linear convergence and optimal complexity of adaptive FEM with inexact solver
Philipp Bringmann, Michael Feischl, Ani Miraci +2
The ultimate goal of any numerical scheme for partial differential equations (PDEs) is to compute an approximation of user-prescribed accuracy at quasi-minimal computational time.…
Scaling-robust built-in a posteriori error estimation for discontinuous least-squares finite element methods
Philipp Bringmann
A convincing feature of least-squares finite element methods is the built-in a posteriori error estimator for any conforming discretization. In order to generalize this property to…
Review and computational comparison of adaptive least-squares finite element schemes
Philipp Bringmann
The convergence analysis for least-squares finite element methods led to various adaptive mesh-refinement strategies: Collective marking algorithms driven by the built-in a posteri…
Local parameter selection in the interior penalty method for the biharmonic equation
Philipp Bringmann, Carsten Carstensen, Julian Streitberger
The symmetric interior penalty method is one of the most popular discontinuous Galerkin methods for the biharmonic equation. This paper introduces an automatic local selectio…
Nonlinear discontinuous Petrov-Galerkin methods
Carsten Carstensen, Philipp Bringmann, Friederike Hellwig +1
The discontinuous Petrov-Galerkin method is a minimal residual method with broken test spaces and is introduced for a nonlinear model problem in this paper. Its lowest-order versio…