Embedded Trefftz DG framework for the analysis of discretizations with local-global decompositions
Numerical Analysis
2025-12-02 v2 Numerical Analysis
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.
Keywords
Cite
@article{arxiv.2412.00806,
title = {Embedded Trefftz DG framework for the analysis of discretizations with local-global decompositions},
author = {Philip L. Lederer and Christoph Lehrenfeld and Paul Stocker and Igor Voulis},
journal= {arXiv preprint arXiv:2412.00806},
year = {2025}
}
Comments
38 pages, 4 figures