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We present a survey of the nonconforming Trefftz virtual element method forthe Laplace and Helmholtz equations. For the latter, we present a new abstractanalysis, based on weaker assumptions on the stabilization, and numericalresults on the dispersion analysis, including comparison with the plane wavediscontinuous Galerkin method.

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