期刊
SIAM JOURNAL ON NUMERICAL ANALYSIS
卷 52, 期 3, 页码 1354-1377出版社
SIAM PUBLICATIONS
DOI: 10.1137/130918149
关键词
space-time finite element method; PDEs posed on surfaces; evolving surfaces
资金
- National Science Foundation [DMS-1315993]
- German Science Foundation (DFG) [RE 1461/4-1]
- Russian Foundation for Basic Research [12-01-00283, 12-01-33084]
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [1315993] Funding Source: National Science Foundation
In this paper, we study numerical methods for the solution of partial differential equations on evolving surfaces. The evolving hypersurface in R-d defines a d-dimensional space-time manifold in the space-time continuum Rd+1. We derive and analyze a variational formulation for a class of diffusion problems on the space-time manifold. For this variational formulation new well-posedness and stability results are derived. The analysis is based on an inf-sup condition and involves some natural, but nonstandard, (anisotropic) function spaces. Based on this formulation a discrete in time variational formulation is introduced that is very suitable as a starting point for a discontinuous Galerkin (DG) space-time finite element discretization. This DG space-time method is explained and results of numerical experiments are presented that illustrate its properties.
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