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A stable space–time finite element method for parabolic evolution problems

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Abstract

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.

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Acknowledgements

The author appreciates the constructive comments from the reviewer which helped improve the article.

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  1. Katholische Hochschulgemeinde der Diözese Linz, Petrinumstrasse 12/8/D220, 4040, Linz, Austria

    Stephen Edward Moore

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  1. Stephen Edward Moore
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Correspondence to Stephen Edward Moore.

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In loving memory of Professor Francis Allotey.

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Moore, S.E. A stable space–time finite element method for parabolic evolution problems. Calcolo 55, 18 (2018). https://doi.org/10.1007/s10092-018-0261-8

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  • DOI: https://doi.org/10.1007/s10092-018-0261-8

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