A convergent finite element algorithm for generalized mean curvature flows of closed surfaces
نویسندگان
چکیده
Abstract An algorithm is proposed for generalized mean curvature flow of closed two-dimensional surfaces, which include inverse and powers flow. Error estimates are proved semidiscretizations full discretizations the The studied here combines evolving surface finite elements, whose nodes determine discrete surface, linearly implicit backward difference formulae time integration. numerical method based on a system coupling evolution to nonlinear second-order parabolic equations normal velocity vector. A convergence proof presented in case elements polynomial degree at least 2 orders 5. error analysis stability consistency yield optimal-order $H^1$-norm bounds computed position, velocity, vector, therefore curvature. performed matrix–vector formulation independent geometric arguments, only enter analysis. Numerical experiments illustrate results also report monotone quantities, e.g. Hawking mass flow, complemented by nonconvex surfaces.
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ژورنال
عنوان ژورنال: Ima Journal of Numerical Analysis
سال: 2021
ISSN: ['1464-3642', '0272-4979']
DOI: https://doi.org/10.1093/imanum/drab043