Discontinuous Galerkin Time Stepping for Subdiffusion Problems

Abstract

Discontinuous Galerkin (DG) time stepping is an alternative to popular schemes for fractional-order problems, such as convolution quadrature and the L1 method (and variants thereof). The talk will be an introduction to DG and its properties, including superconvergence behaviour at the local Radau points. The numerical analysis for DG schemes applied to classical ODEs and to parabolic PDEs is well-developed, but plenty of open questions remain for subdiffusion equations.