5 papers
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 optimal complexity of adaptive iteratively linearized FEM for nonlinear PDEs
Ani Miraçi, Dirk Praetorius, Julian Streitberger
We propose an adaptive iteratively linearized finite element method (AILFEM) in the context of strongly monotone nonlinear operators in Hilbert spaces. The approach combines adapti…
Cost-optimal adaptive FEM with linearization and algebraic solver for semilinear elliptic PDEs
Maximilian Brunner, Dirk Praetorius, Julian Streitberger
We consider scalar semilinear elliptic PDEs, where the nonlinearity is strongly monotone, but only locally Lipschitz continuous. To linearize the arising discrete nonlinear problem…
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.…
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…