The nonconforming Trefftz virtual element method: general setting, applications, and dispersion analysis for the Helmholtz equation

TL;DR

This paper surveys the nonconforming Trefftz virtual element method for Laplace and Helmholtz equations, introduces a new abstract analysis with weaker stabilization assumptions, and compares dispersion analysis results with plane wave discontinuous Galerkin methods.

Contribution

It provides a comprehensive overview of the method and introduces a novel abstract analysis framework for the Helmholtz equation with less restrictive stabilization assumptions.

Findings

Dispersion analysis results show competitive performance.

New abstract analysis extends theoretical understanding.

Comparison with plane wave DG highlights advantages.

Abstract

We present a survey of the nonconforming Trefftz virtual element method for the Laplace and Helmholtz equations. For the latter, we present a new abstract analysis, based on weaker assumptions on the stabilization, and numerical results on the dispersion analysis, including comparison with the plane wave discontinuous Galerkin method.