Authors: Dominicus, Alexander
Gaspoz, Fernando
Kreuzer, Christian
Title: Convergence of adaptive C0-interior penalty Galerkin method for the biharmonic problem
Language (ISO): en
Abstract: We develop a basic convergence analysis for an adaptive C0IPG method for the Biharmonic problem which provides convergence without rates for all practically relevant marking strategies and all penalty parameters assuring coercivity of the method. The analysis hinges on embedding properties of (broken) Sobolev and BV spaces, and the construction of a suitable limit space. In contrast to the convergence result of adaptive discontinuous Galerkin methods for elliptic PDEs, by Kreuzer and Georgoulis, here we have to deal with the fact that the Lagrange finite element spaces may possibly contain no proper C1-conforming subspace. This prevents from a straight forward generalisation and requires the development of some new key technical tools.
Subject Headings: adaptive discontinuous Galerkin methods
quadratic C0-interior penalty method
biharmonic problem
Issue Date: 2019-01
Appears in Collections:Ergebnisberichte des Instituts für Angewandte Mathematik

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