76 citations · 1.5k across the 82 of their papers we have counts for
7 papers · 2 filters
Convergence of adaptive stochastic Galerkin FEM
Alex Bespalov, Dirk Praetorius, Leonardo Rocchi +1
We propose and analyze novel adaptive algorithms for the numerical solution of elliptic partial differential equations with parametric uncertainty. Four different marking strategie…
Iterative solution and preconditioning for the tangent plane scheme in computational micromagnetics
Johannes Kraus, Carl-Martin Pfeiler, Dirk Praetorius +2
The tangent plane scheme is a time-marching scheme for the numerical solution of the nonlinear parabolic Landau-Lifshitz-Gilbert equation (LLG), which describes the time evolution…
Optimal additive Schwarz preconditioning for adaptive 2D IGA boundary element methods
Thomas Führer, Gregor Gantner, Dirk Praetorius +1
We define and analyze (local) multilevel diagonal preconditioners for isogeometric boundary elements on locally refined meshes in two dimensions. Hypersingular and weakly-singular…
Adaptive BEM with optimal convergence rates for the Helmholtz equation
Alex Bespalov, Timo Betcke, Alexander Haberl +1
We analyze an adaptive boundary element method for the weakly-singular and hypersingular integral equations for the 2D and 3D Helmholtz problem. The proposed adaptive algorithm is…
Goal-oriented error estimation and adaptivity for elliptic PDEs with parametric or uncertain inputs
Alex Bespalov, Dirk Praetorius, Leonardo Rocchi +1
We use the ideas of goal-oriented error estimation and adaptivity to design and implement an efficient adaptive algorithm for approximating linear quantities of interest derived fr…
Adaptive BEM with inexact PCG solver yields almost optimal computational costs
Thomas Führer, Alexander Haberl, Dirk Praetorius +1
We consider the preconditioned conjugate gradient method (PCG) with optimal preconditioner in the frame of the boundary element method (BEM) for elliptic first-kind integral equati…
Optimal convergence behavior of adaptive FEM driven by simple (h-h/2)-type error estimators
Christoph Erath, Gregor Gantner, Dirk Praetorius
For some Poisson-type model problem, we prove that adaptive FEM driven by the (h-h/2)-type error estimators from [Ferraz-Leite, Ortner, Praetorius, Numer. Math. 116 (2010)] leads t…