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.
- 8.Ladyzhenskaya, O.A., Solonnikov, V.A., Uraltseva, N.N.: Linear and quasilinear equations of parabolic type. Nauka, Moscow, 1967. In: Russian. Translated in AMS, Providence, RI (1968)Google Scholar
- 9.Langer, U., Matculevich, S., Repin, S.: A posteriori error estimates for space–time iga approximations to parabolic initial boundary value problems. arxiv, (2017-14). arXiv:1612.08998
- 11.Moore, S.E.: Nonstandard Discretization Strategies in Isogeometric Analysis for Partial Differential Equations. PhD thesis, Johannes Kepler University (2017)Google Scholar
- 12.Moore, S.E.: Space–time multipatch discontinuous galerkin isogeometric analysis for parabolic evolution problem. arxiv (2017)Google Scholar
- 13.Neumüller, M.: Space–time methods: fast solvers and applications, volume 20 of monographic series TU Graz: Computation in Engineering and Science. TU Graz (2013)Google Scholar
- 17.Tezduyar, T.E., Behr, M., Mittal, S., Liou, J.: A new strategy for finite element computations involving moving boundaries and interfaces—the deforming-spatial-domain/space-time procedure. I: the concept and the preliminary numerical tests. Comput. Methods Appl. Mech. Eng. 94(3), 339–351 (1992)MathSciNetCrossRefzbMATHGoogle Scholar
- 18.Tezduyar, T.E., Behr, M., Mittal, S., Liou, J.: A new strategy for finite element computations involving moving boundaries and interfaces—the deforming-spatial-domain/space-time procedure: II. Computation of free-surface flows, two-liquid flows, and flows with drifting cylinders. Comput. Methods Appl. Mech. Eng. 94(3), 353–371 (1992)MathSciNetCrossRefzbMATHGoogle Scholar