5 papers · 1 filter
Adaptive finite element methods with optimally preconditioned GMRES guarantee optimal complexity
Thomas Führer, Paula Hilbert, Ani Miraçi +1
We analyze optimal complexity of adaptive finite element methods (AFEMs) for general second-order linear elliptic partial differential equations (PDEs) in the Lax-Milgram setting.…
Generalized preconditioned conjugate gradients for adaptive FEM with optimal complexity
Paula Hilbert, Ani Miraçi, Dirk Praetorius
We consider adaptive finite element methods (AFEMs) with inexact algebraic solvers for second-order symmetric linear elliptic diffusion problems. Optimal complexity of AFEM, i.e.,…
A-posteriori-steered -robust multigrid and domain decomposition methods with optimal step-sizes for mixed finite element discretizations of elliptic problems
Ani Miraçi, Jan Papež, Martin Vohralík +1
In this work, we develop algebraic solvers for linear systems arising from the discretization of second-order elliptic partial differential equations by saddle-point mixed finite e…
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…
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.…