Beschle, Cedric Aaron and Kovacs, Balazs (2022) Stability and error estimates for non-linear Cahn-Hilliard-type equations on evolving surfaces. NUMERISCHE MATHEMATIK, 151 (1). pp. 1-48. ISSN 0029-599X, 0945-3245
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In this paper, we consider a non-linear fourth-order evolution equation of Cahn-Hilliard-type on evolving surfaces with prescribed velocity, where the non-linear terms are only assumed to have locally Lipschitz derivatives. High-order evolving surface finite elements are used to discretise the weak equation system in space, and a modified matrix-vector formulation for the semi-discrete problem is derived. The anti-symmetric structure of the equation system is preserved by the spatial discretisation. A new stability proof, based on this structure, combined with consistency bounds proves optimal-order and uniform-in-time error estimates. The paper is concluded by a variety of numerical experiments.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | PARABOLIC DIFFERENTIAL-EQUATIONS; FINITE-ELEMENT APPROXIMATION; TIME DISCRETIZATION; ENERGY; PDES; 65M60; 35R01; 35K55; 65M12; 65M15 |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Harald Garcke |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 08 Feb 2024 15:34 |
| Last Modified: | 08 Feb 2024 15:34 |
| URI: | https://pred.uni-regensburg.de/id/eprint/57816 |
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