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…
Quasi-optimal complexity of iterative Galerkin methods driven by an elliptic reconstruction error estimator
Maximilian Brunner, Gregor Gantner, Christoph Lietz +1
We study an iterative Galerkin method for quasilinear elliptic problems in the Browder-Minty setting. The resulting discrete nonlinear systems are solved by linearization via a (da…
On -robust convergence and optimality of adaptive FEM driven by equilibrated-flux estimators
Théophile Chaumont-Frelet, Zhaonan Dong, Gregor Gantner +1
Building on existing -adaptive algorithms driven by equilibrated-flux estimators from [ESAIM Math. Model. Numer. Anal. 57 (2023), 329--366] and the references therein, we propo…
Optimal convergence rates of an adaptive finite element method for unbounded domains
Théophile Chaumont-Frelet, Gregor Gantner
We consider linear reaction-diffusion equations posed on unbounded domains, and discretized by adaptive Lagrange finite elements. To obtain finite-dimensional spaces, it is necessa…
Adaptive boundary element methods for regularized combined field integral equations
Théophile Chaumont-Frelet, Gregor Gantner
While the exterior Helmholtz problem with Dirichlet boundary conditions is always well-posed, the associated standard boundary integral equations are not if the squared wavenumber…