The discrete plateau problem: Convergence results

DOI10.1090/S0025-5718-99-01026-1zbMath1043.65126MaRDI QIDQ4235505

Gerhard Dziuk, John E. Hutchinson

Publication date: 22 March 1999

Published in: Mathematics of Computation (Search for Journal in Brave)

zbMATH Keywords

finite elementsorder of convergenceMinimal surfacePlateau Problem

Mathematics Subject Classification ID

Minimal surfaces and optimization (49Q05) Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30)

Related Items (15)

Finite element approximations to surfaces of prescribed variable mean curvature ⋮ An algorithm for prescribed mean curvature using isogeometric methods ⋮ On the numerical solution of Plateau's problem ⋮ 𝐿²-estimate for the discrete Plateau Problem ⋮ Finite Element Approximation of Conformal Mappings to Unbounded Jordan Domains ⋮ On the convergence of metric and geometric properties of polyhedral surfaces ⋮ Variational convergence of discrete minimal surfaces ⋮ Approximation of minimal surfaces with free boundaries ⋮ Numerical methods for biomembranes: Conforming subdivision methods versus non-conforming PL methods ⋮ Variational Methods for Discrete Geometric Functionals ⋮ Finite element approximations of minimal surfaces: algorithms and mesh refinement ⋮ High order numerical approximation of minimal surfaces ⋮ Discrete duality finite volume method with tangential redistribution of points for surfaces evolving by mean curvature ⋮ Learning phase field mean curvature flows with neural networks ⋮ The discrete Plateau Problem: Algorithm and numerics

Cites Work

• On the approximation of unstable parametric minimal surfaces
• An Iterative Method for Elliptic Problems on Regions Partitioned into Substructures
• The discrete Plateau Problem: Algorithm and numerics
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