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 language | English |
|---|---|
| Pages (from-to) | 1365-1385 |
| Number of pages | 21 |
| Journal | IMA Journal of Numerical Analysis |
| Volume | 33 |
| Issue number | 4 |
| DOIs | |
| Publication status | Published - Oct 2013 |
Keywords
- parabolic PDE
- evolving-surface finite element method
- backward difference formula
- G-stability
- multiplier technique
- energy estimates
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