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Finite element approximations of minimal surfaces: algorithms and mesh refinement. (arXiv:1706.09672v1 [math.NA])
来源于:arXiv
Finite element approximations of minimal surface 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. 查看全文>>