The discrete Plateau Problem: Algorithm and numerics

DOI10.1090/S0025-5718-99-01025-XzbMath0913.65062MaRDI QIDQ4221966

Gerhard Dziuk, John E. Hutchinson

Publication date: 3 December 1998

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

zbMATH Keywords

algorithmconvergencefinite elementsminimal surfaceplateau problemnumerial results

Mathematics Subject Classification ID

Numerical optimization and variational techniques (65K10) Newton-type methods (49M15) Minimal surfaces and optimization (49Q05) Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10)

Related Items (19)

Finite element approximations to surfaces of prescribed variable mean curvature ⋮ On the numerical solution of Plateau's problem ⋮ An approximation method based on MRA for the quasi-Plateau problem ⋮ 𝐿²-estimate for the discrete Plateau Problem ⋮ Finite Element Approximation of Conformal Mappings to Unbounded Jordan Domains ⋮ The \(C^1\) and \(C^2\) quasi-Plateau problems ⋮ A robust construction of minimal surface from a general initial mesh ⋮ Simulation of a Soap Film Möbius Strip Transformation ⋮ Discrete Minimal Surfaces of Koebe Type ⋮ 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 ⋮ A numerical method for computing minimal surfaces in arbitrary dimension ⋮ Nonlinear hyperbolic equations in surface theory: Integrable discretizations and approximation results ⋮ Learning phase field mean curvature flows with neural networks ⋮ The discrete plateau problem: Convergence results

Uses Software

• Surface Evolver

Cites Work

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• Numerical Solution of the Minimal Surface Equation

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