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• W3046194559 abstract "A proof of convergence is given for a novel evolving surface finite element semi-discretization of Willmore flow of closed two-dimensional surfaces, and also of surface diffusion flow. The numerical method proposed and studied here discretizes fourth-order evolution equations for the normal vector and mean curvature, reformulated as a system of second-order equations, and uses these evolving geometric quantities in the velocity law interpolated to the finite element space. This numerical method admits a convergence analysis in the case of continuous finite elements of polynomial degree at least two. The error analysis combines stability estimates and consistency estimates to yield optimal-order $H^1$-norm error bounds for the computed surface position, velocity, normal vector and mean curvature. The stability analysis is based on the matrix--vector formulation of the finite element method and does not use geometric arguments. The geometry enters only into the consistency estimates. Numerical experiments illustrate and complement the theoretical results." @default.
• W3046194559 created "2020-08-03" @default.
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• W3046194559 date "2020-07-30" @default.
• W3046194559 modified "2023-09-27" @default.
• W3046194559 title "A convergent evolving finite element algorithm for Willmore flow of closed surfaces" @default.
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• W3046194559 hasPublicationYear "2020" @default.
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