Name
Abstract | ||
|---|---|---|
We present a new high-order finite element method for the discretization of partial differential equations on stationary smooth surfaces which are implicitly described as the zero level of a level set function. The discretization is based on a trace finite element technique. The higher discretization accuracy is obtained by using an isoparametric mapping of the volume mesh, based on the level set function, as introduced in [C. Lehrenfeld, Comp. Meth. Appl. Mech. Engrg., 300 (2016), pp. 716-733]. The resulting trace finite element method is easy to implement. We present an error analysis of this method and derive optimal order H-1 (Gamma)-norm error bounds. A second topic of this paper is a unified analysis of several stabilization methods for trace finite element methods. Only a stabilization method which is based on adding an anisotropic diffusion in the volume mesh is able to control the condition number of the stiffness matrix also for the case of higher-order discretizations. Results of numerical experiments are included which con firm the theoretical findings on optimal order discretization errors and uniformly bounded condition numbers. |
Year | DOI | Venue |
|---|---|---|
2018 | 10.1137/16M1102203 | SIAM JOURNAL ON NUMERICAL ANALYSIS |
Keywords | Field | DocType |
trace finite element method,isoparametric finite element method,high-order methods,geometry errors,conditioning,surface PDEs | Boundary knot method,Mathematical optimization,Mathematical analysis,Extended finite element method,Finite element method,Finite volume method,hp-FEM,Mathematics,Mixed finite element method,Smoothed finite element method,Spectral element method | Journal |
Volume | Issue | ISSN |
56 | 1 | 0036-1429 |
Citations | PageRank | References |
3 | 0.48 | 1 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Jörg Grande | 1 | 36 | 4.92 |
| Christoph Lehrenfeld | 2 | 46 | 7.55 |
| Arnold Reusken | 3 | 305 | 44.91 |