Embedded Trefftz DG framework for the analysis of discretizations with local-global decompositions

Abstract

This paper presents a framework for the analysis of discretization methods based on the decomposition into local and global problems. We apply the framework to provide a comprehensive error analysis for the embedded Trefftz discontinuous Galerkin method, for a wide range of second-order scalar elliptic partial differential equations and a scalar reaction-advection problem. We also analyze quasi-Trefftz methods with our framework, presenting the first optimal error bounds in weaker norms.