A stable space–time finite element method for parabolic evolution problems
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This paper is concerned with the analysis of a new stable space–time finite element method (FEM) for the numerical solution of parabolic evolution problems in moving spatial computational domains. The discrete bilinear form is elliptic on the FEM space with respect to a discrete energy norm. This property together with a corresponding boundedness property, consistency and approximation results for the FEM spaces yield an a priori discretization error estimate with respect to the discrete norm. Finally, we confirm the theoretical results with numerical experiments in spatial moving domains.
KeywordsFinite element method space–time Parabolic evolution problem Moving spatial computational domains A priori discretization error estimates
Mathematics Subject Classification65M12 65M60
The author appreciates the constructive comments from the reviewer which helped improve the article.
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