DeepAI AI Chat
Log In Sign Up

Convergence of an adaptive C^0-interior penalty Galerkin method for the biharmonic problem

by   Alexander Dominicus, et al.

We develop a basic convergence analysis for an adaptive C^0IPG 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 [Math. Comp. 87 (2018), no. 314, 2611–2640], here we have to deal with the fact that the Lagrange finite element spaces may possibly contain no proper C^1-conforming subspace. This prevents from a straight forward generalisation and requires the development of some new key technical tools.


page 1

page 2

page 3

page 4


Convergence and optimality of an adaptive modified weak Galerkin finite element method

An adaptive modified weak Galerkin method (AmWG) for an elliptic problem...

Implementation of hp-adaptive discontinuous finite element methods in Dune-Fem

In this paper we describe generic algorithms and data structures for the...

Uniform subspace correction preconditioners for discontinuous Galerkin methods with hp-refinement

In this paper, we develop subspace correction preconditioners for discon...

Convergence analysis of oversampled collocation boundary element methods in 2D

Collocation boundary element methods for integral equations are easier t...

Stable implementation of adaptive IGABEM in 2D in MATLAB

We report on our MATLAB program package IGABEM2D, which provides an easi...