An Anisotropic hp-mesh Adaptation Method for Time-Dependent Problems Based on Interpolation Error Control

Abstract

We propose an efficient mesh adaptive method for the numerical solution of time-dependent partial differential equations considered in the fixed space-time cylinder Ω×(0,T). We employ the space-time discontinuous Galerkin method which enables us to use different meshes at different time levels in a natural way. The mesh adaptive algorithm is based on control of the interpolation error in the L∞(0,T;Lq(Ω))-norm.