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Medientyp:
E-Artikel
Titel:
Unfitted Trefftz discontinuous Galerkin methods for elliptic boundary value problems
Beteiligte:
Heimann, Fabian;
Lehrenfeld, Christoph;
Stocker, Paul;
von Wahl, Henry
Erschienen:
EDP Sciences, 2023
Erschienen in:ESAIM: Mathematical Modelling and Numerical Analysis
Sprache:
Nicht zu entscheiden
DOI:
10.1051/m2an/2023064
ISSN:
2822-7840;
2804-7214
Entstehung:
Anmerkungen:
Beschreibung:
<jats:p>We propose a new geometrically unfitted finite element method based on discontinuous Trefftz ansatz spaces. Trefftz methods allow for a reduction in the number of degrees of freedom in discontinuous Galerkin methods, thereby, the costs for solving arising linear systems significantly. This work shows that they are also an excellent way to reduce the number of degrees of freedom in an unfitted setting. We present a unified analysis of a class of geometrically unfitted discontinuous Galerkin methods with different stabilisation mechanisms to deal with small cuts between the geometry and the mesh. We cover stability and derive a-priori error bounds, including errors arising from geometry approximation for the class of discretisations for a model Poisson problem in a unified manner. The analysis covers Trefftz and full polynomial ansatz spaces, alike. Numerical examples validate the theoretical findings and demonstrate the potential of the approach.</jats:p>