Rate optimality of adaptive finite element methods with respect to overall computational costs

G Gantner, A Haberl, D Praetorius… - Mathematics of …, 2021‏ - ams.org
We consider adaptive finite element methods for second-order elliptic PDEs, where the
arising discrete systems are not solved exactly. For contractive iterative solvers, we …

Optimal preconditioning for the symmetric and nonsymmetric coupling of adaptive finite elements and boundary elements

M Feischl, T Führer, D Praetorius… - Numerical Methods for …, 2017‏ - Wiley Online Library
We analyze a multilevel diagonal additive Schwarz preconditioner for the adaptive coupling
of FEM and BEM for a linear 2D Laplace transmission problem. We rigorously prove that the …

Optimal additive Schwarz preconditioning for hypersingular integral equations on locally refined triangulations

M Feischl, T Führer, D Praetorius, EP Stephan - Calcolo, 2017‏ - Springer
For the non-preconditioned Galerkin matrix of the hypersingular integral operator, the
condition number grows with the number of elements as well as the quotient of the maximal …

Stable multilevel splittings of boundary edge element spaces

R Hiptmair, S Mao - BIT Numerical Mathematics, 2012‏ - Springer
We establish the stability of nodal multilevel decompositions of lowest-order conforming
boundary element subspaces of the trace space H^-12(div_\varGamma,\varGamma) of …

[PDF][PDF] Zur Kopplung von finiten Elementen und Randelementen

T Führer - 2014‏ - mat.uc.cl
Für nichtlineare Laplace-und Lamé-Transmissionsprobleme betrachten wir die
symmetrische als auch verschiedene Varianten der nicht-symmetrischen Kopplung von FEM …

BPX preconditioners for isogeometric analysis using (truncated) hierarchical B-splines

C Bracco, D Cho, C Giannelli, R Vázquez - Computer Methods in Applied …, 2021‏ - Elsevier
We present the construction of additive multilevel preconditioners, also known as BPX
preconditioners, for the solution of the linear system arising in isogeometric adaptive …

[HTML][HTML] Adaptive finite element analysis of elliptic problems based on bubble-type local mesh generation

W Zhang, Y Nie, Y Gu - Journal of Computational and Applied Mathematics, 2015‏ - Elsevier
A new mesh adaptivity algorithm that combines a posteriori error estimation with bubble-type
local mesh generation (BLMG) strategy for elliptic differential equations is proposed. The …

[HTML][HTML] Optimal additive Schwarz methods for the hp-BEM: the hypersingular integral operator in 3D on locally refined meshes

T Führer, JM Melenk, D Praetorius, A Rieder - Computers & Mathematics …, 2015‏ - Elsevier
We propose and analyze an overlap** Schwarz preconditioner for the p and hp boundary
element method for the hypersingular integral equation in 3D. We consider surface …

An improved multigrid algorithm for n-irregular meshes with subspace correction smoother

E Aulisa, S Calandrini, G Capodaglio - Computers & Mathematics with …, 2018‏ - Elsevier
We propose a multigrid V-cycle algorithm for locally refined meshes with arbitrary hanging
node configurations. Unlike existing algorithms that perform smoothing only on a subspace …

Local multilevel methods for adaptive finite element methods for nonsymmetric and indefinite elliptic boundary value problems

H Chen, X Xu - SIAM journal on numerical analysis, 2010‏ - SIAM
In this paper, we propose some local multilevel algorithms for solving linear systems arising
from adaptive finite element approximations of nonsymmetric and indefinite elliptic boundary …