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

2024/12/01 by Lederer, Philip L., Lehrenfeld, Christoph, Stocker, Paul +1
#FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2412.00806

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.

Related

• Embedded Trefftz discontinuous Galerkin methods
• Polynomial quasi-Trefftz DG for PDEs with smooth coefficients: elliptic problems
• A quasi-Trefftz discontinuous Galerkin method for the homogeneous diffusion-advection-reaction equation with piecewise-smooth coefficients
• Local Taylor-based polynomial quasi-Trefftz spaces for scalar linear equations
• A Trefftz polynomial space-time discontinuous Galerkin method for the\n second order wave equation