SIAM Journal on Numerical Analysis
Natural minimal surfaces (videotape): via theory and computation
Natural minimal surfaces (videotape): via theory and computation
Error estimates on a new nonlinear Galerkin method based on two-grid finite elements
SIAM Journal on Numerical Analysis
Some new error estimates for Ritz-Galerkin methods with minimal regularity assumptions
Mathematics of Computation
Two-grid Discretization Techniques for Linear and Nonlinear PDEs
SIAM Journal on Numerical Analysis
Local and parallel finite element algorithms based on two-grid discretizations
Mathematics of Computation
Finite Element Method for Elliptic Problems
Finite Element Method for Elliptic Problems
Generating Minimal Surfaces Subject to the Plateau Problems by Finite Element Method
NMA '02 Revised Papers from the 5th International Conference on Numerical Methods and Applications
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This paper talks about generating the minimal surfaces which are subject to the well-known Plateau problem. The differential form of the Plateau problem is defined at first and, its associated discrete schemes which reduced from the finite element methods could be practically solved by the numerical iteration methods like the Newton's iteration. The convergence property of the finite element solutions are proved by steps and some multi-grid algorithms have been implemented to speed up the computation. These new approximation methods will be applied to the project of generating the minimal surfaces on computer softwares later.