Anisotropic hp-adaptive discontinuous Galerkin method for the numerical solution of time dependent PDEs

• ID: 2692, RIV: 10301813
• ISSN: 0096-3003, ISBN: not specified
• source: Applied Mathematics and Computation
• keywords: Anisotropic hp-adaptation; discontinuous Galerkin method; numerical solution; time dependent PDEs
• authors: Vít Dolejší
• authors from KNM: Dolejší Vít

Abstract

We deal with the numerical solution of time dependent problems with the aid of anisotropic $hp$-grids. We present an algorithm which generates a sequence of anisotropic triangular grids and the corresponding polynomial approximation degrees in such a way that the interpolation error measured in the discrete $L^\infty(0,T; L^q(\Omega))$-norm ($q\in[1,\infty]$ and $\Omega\subset\mathbb{R}^2$) is under a given tolerance and the number of degrees of freedom is as small as possible. The efficiency of the algorithm is demonstrated by numerical experiments.