Unfitted Trefftz discontinuous Galerkin methods for elliptic boundary value problems
arXiv:2212.12236 · doi:10.1051/m2an/2023064
Abstract
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.
References in corpus (7)
- High order unfitted finite element methods on level set domains using isoparametric mappings
- The aggregated unfitted finite element method for elliptic problems
- Higher-order meshing of implicit geometries - part I: Integration and interpolation in cut elements
- CutIGA with Basis Function Removal
- A stabilized cut discontinuous Galerkin framework: I. Elliptic boundary value and interface problems
- Linking ghost penalty and aggregated unfitted methods
- Unfitted Trefftz discontinuous Galerkin methods for elliptic boundary value problems