522
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RWTH Publication No: 861858 2022   IGPM522.pdf |
TITLE |
An accurate and robust Eulerian finite element method for partial differential equations on evolving surfaces
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AUTHORS |
Hauke Sass, Arnold Reusken |
ABSTRACT |
In this paper we present a new Eulerian finite element method for the discretization
of scalar partial differential equations on evolving surfaces. In this method we use the restriction
of standard space-time finite element spaces on a fixed bulk mesh to the space-time surface. The
structure of the method is such that it naturally fits to a level set representation of the evolving surface. The higher order version of the method is based on a space-time variant of a mesh deformation
that has been developed in the literature for stationary surfaces. The discretization method that we
present is of (optimal) higher order accuracy for smoothly varying surfaces with sufficiently smooth
solutions. Without any modifications the method can be used for the discretization of problems with
topological singularities. A numerical study demonstrates both the higher order accuracy for smooth
cases and the robustness with respect to toplogical singularities. |
KEYWORDS |
surface partial differential equation, trace finite element method, space-time finite element method, unfitted finite element method |
DOI |
10.1016/j.camwa.2023.06.040 |
PUBLICATION |
Computers & Mathematics with Applications, Volume 146, 15 September 2023, Pages 253-270 |