We present a survey of the nonconforming Trefftz virtual element method for the Laplace and Helmholtz equations. As for the latter, we show 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.
Mascotto, L., Perugia, I., Pichler, A. (2022). The Nonconforming Trefftz Virtual Element Method: General Setting, Applications, and Dispersion Analysis for the Helmholtz Equation. In P.F. Antonietti, L. Beirão da Veiga, G. Manzini (a cura di), The Virtual Element Method and its Applications (pp. 363-410). Springer [10.1007/978-3-030-95319-5_9].
The Nonconforming Trefftz Virtual Element Method: General Setting, Applications, and Dispersion Analysis for the Helmholtz Equation
Mascotto, L
;
2022
Abstract
We present a survey of the nonconforming Trefftz virtual element method for the Laplace and Helmholtz equations. As for the latter, we show 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.
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