Backward difference time discretization of parabolic differential equations on evolving surfaces

Christian Lubich*, Dhia Mansour, Chandrasekhar Venkataraman

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

36 Citations (Scopus)

Abstract

A linear parabolic differential equation on a moving surface is discretized in space by evolving-surface finite elements and in time by backward difference formulas (BDFs). Using results from Dahlquist's G-stability theory and Nevanlinna & Odeh's multiplier technique together with properties of the spatial semidiscretization, stability of the full discretization is proved for BDF methods up to order 5 and optimal-order convergence is shown. Numerical experiments illustrate the behaviour of the fully discrete method.

Original languageEnglish
Pages (from-to)1365-1385
Number of pages21
JournalIMA Journal of Numerical Analysis
Volume33
Issue number4
DOIs
Publication statusPublished - Oct 2013

Keywords

  • parabolic PDE
  • evolving-surface finite element method
  • backward difference formula
  • G-stability
  • multiplier technique
  • energy estimates

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