Abstract
Finite element approximations of minimal surfaces are not always precise. They can even sometimes completely collapse. In this paper, we provide a simple and inexpensive method, in terms of computational cost, to improve finite element approximations of minimal surfaces by local boundary mesh refinements. By highlighting the fact that a collapse is simply the limit case of a locally bad approximation, we show that our method can also be used to avoid the collapse of finite element approximations. We also extend the study of such approximations to partially free boundary problems and give a theorem for their convergence. Numerical examples showing improvements induced by the method are given throughout the paper.
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The authors would like to thank the anonymous reviewers for their valuable comments and suggestions to improve the quality of the article.
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Grodet, A., Tsuchiya, T. Finite element approximations of minimal surfaces: algorithms and mesh refinement. Japan J. Indust. Appl. Math. 35, 707–725 (2018). https://doi.org/10.1007/s13160-018-0303-2
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DOI: https://doi.org/10.1007/s13160-018-0303-2