Linearly implicit full discretization of surface evolution

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Abstract

Stability and convergence of full discretizations of various surface evolution equations are studied in this paper. The proposed discretization combines a higher-order evolving-surface finite element method for space discretization with higher-order linearly implicit backward difference formulae for time discretization. The stability of the full discretization is studied in the matrix–vector formulation of the numerical method. The geometry of the problem enters into the bounds of the consistency errors, but does not enter into the proof of stability. Numerical examples illustrate the convergence behaviour of the full discretization.

Mathematics Subject Classification

35R01 65M60 65M15 65M12 

Notes

Acknowledgements

This work is supported by Deutsche Forschungsgemeinschaft, SFB 1173.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Mathematisches InstitutUniversität TübingenTübingenGermany

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