Journal
SIAM JOURNAL ON NUMERICAL ANALYSIS
Volume 59, Issue 6, Pages 2823-2842Publisher
SIAM PUBLICATIONS
DOI: 10.1137/21M1391626
Keywords
curve shortening flow; fully discrete; linearly implicit; convergence; error estimate
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Funding
- National Natural Science Foundation of China [51739007]
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In this paper, it is proved that Dziuk's fully discrete linearly implicit scheme has an optimal error estimate in the H-1 norm for curve shortening flow.
Convergence of Dziuk's fully discrete linearly implicit scheme which was proposed in [G. Dziuk, Math. Models Methods Appl. At., 4 (1994), pp. 589-606] for curve shortening flow still remains open. In this paper, we prove that this scheme has an optimal error estimate in the H-1-norm.
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