MS 1: Adaptive Finite Element Methods

Organizers

Abstract

This mini-symposium reflects the latest developments on the convergence of adaptive finite element methods in computational science and engineering. Optimal convergence rates with respect to the number of degrees of freedom, and the concept of nonlinear approximation classes will be discussed. The start is with an axiomatic approach for stationary problems, followed by some novel results on instance optimality for the maximum marking strategy. Time depending problems are addressed in the situation of a adaptive strategy for the heat equation, and first results will presented on a space-time discontinuous Galerkin discretisation for the Maxwell’ equations. The mini-symposium hence covers various hot aspects of adaptivity in CPDEs.

List of speakers

  • Dirk Praetorius (Vienna UT, Austria):
    Rate optimality of adaptive algorithms: An axiomatic approach
  • Lars Diening (LMU, Germany):
    Instance optimality of the maximum strategy
  • Christian Kreuzer (Ruhr U Bochum, Germany):
    Design and convergence analysis for an adaptive discretization of the heat equation
  • Willy Doerfler (KIT, Germany):
    An adaptive space-time discontinuous Galerkin method for Maxwell's equations

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