On the approximation of unstable parametric minimal surfaces

DOI10.1007/BF01322308zbMath0853.65074MaRDI QIDQ1904101

John E. Hutchinson, Gerhard Dziuk

Publication date: 8 December 1996

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

zbMATH Keywords

finite element methodboundary element methodsemi-discrete minimal surfaceunstable parametric minimal surfaces

Mathematics Subject Classification ID

Numerical optimization and variational techniques (65K10) Minimal surfaces and optimization (49Q05)

Related Items

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, On the numerical approximation and computation of minimal surface continua bounded by one-parameter families of polygonal contours, A numerical method for computing minimal surfaces in arbitrary dimension, Numerical Finiteness Results for Minimal Surfaces in Three-Dimensional Space Forms, The discrete Plateau Problem: Algorithm and numerics, The discrete plateau problem: Convergence results

Uses Software

• Surface Evolver

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• An algorithm for evolutionary surfaces
• On discrete Dirichlet and Plateau problems
• The index theorem for classical minimal surfaces
• A contribution to the numerical approximation of minimal surfaces
• Consideration of obstacles in the numerical approximation of minimal surfaces
• Boundary behavior of minimal surfaces
• A proof of the regularity everywhere of the classical solution to Plateau's problem
• The boundary behavior of minimal surfaces. Kellogg's theorem and branch points on the boundary
• Regularity of minimizing surfaces of prescribed mean curvature
• Verzweigungspunkte von H-Flächen. I
• Verzweigungspunkte von H-Flächen. II
• The existence of minimal surfaces of general critical types
• The Plateau problem for non-relative minima
• On a critical point theory for minimal surfaces spanning a wire in Rn.
• Discrete Solution of the Plateau Problem and its Convergence
• Explicit determination of area minimizing hypersurfaces. II
• On the Numerical Treatment of Quasiminimal Surfaces
• Computing Discrete Minimal Surfaces and Their Conjugates
• A Note on Discrete Solutions of the Plateau Problem
• The Surface Evolver
• Numerical Solution of the Minimal Surface Equation