Journal ArticleDOI
Numerical solutions of a two-phase membrane problem
Reads0
Chats0
TLDR
In this paper, different numerical methods for a two-phase free boundary problem are discussed and an efficient algorithm based on the finite element method is presented, which converges to the solution of the given free boundary problems.About:
This article is published in Applied Numerical Mathematics.The article was published on 2011-01-01. It has received 22 citations till now. The article focuses on the topics: Boundary knot method & Free boundary problem.read more
Citations
More filters
Journal ArticleDOI
An L^1 Penalty Method for General Obstacle Problems
TL;DR: An efficient numerical scheme for solving obstacle problems in divergence form based on a reformulation of the obstacle in terms of an $L^1$-like penalty on the variational problem that works for nonlinear variational inequalities arising from convex minimization problems.
Journal ArticleDOI
An adaptive wavelet collocation method for solving optimal control of elliptic variational inequalities of the obstacle type
TL;DR: An adaptive wavelet collocation method is used and the fast wavelet transform of compact-supported interpolating wavelets is taken to develop a multi-level algorithm, which generates an adaptive computational grid that takes less CPU time than using a full regular mesh.
Journal ArticleDOI
A Posteriori Error Estimates for Two-Phase Obstacle Problem
Sergey Repin,Jan Valdman +1 more
TL;DR: Uraltseva as discussed by the authors derived a computable majorant valid for any function in the admissible (energy) class of functions and proved that the majorant vanishes if and only if the function coincides with the minimizer.
Journal ArticleDOI
Error identities for variational problems with obstacles: Error identities for variational problems with obstacles
Posted Content
An L1 Penalty Method for General Obstacle Problems
TL;DR: In this paper, an exact regularization of the obstacle in terms of an L 1-like penalty on the variational problem is proposed to solve the free boundary inherent in the obstacle problem without any need for problem specific or complicated discretization.
References
More filters
Book
Elliptic Partial Differential Equations of Second Order
David Gilbarg,Neil S. Trudinger +1 more
TL;DR: In this article, Leray-Schauder and Harnack this article considered the Dirichlet Problem for Poisson's Equation and showed that it is a special case of Divergence Form Operators.
Book
The Mathematical Theory of Finite Element Methods
TL;DR: In this article, the construction of a finite element of space in Sobolev spaces has been studied in the context of operator-interpolation theory in n-dimensional variational problems.
Book
Convex analysis and variational problems
Ivar Ekeland,Roger Téman +1 more
TL;DR: In this article, the authors consider non-convex variational problems with a priori estimate in convex programming and show that they can be solved by the minimax theorem.
Book
The Linear Complementarity Problem
TL;DR: In this article, the authors present an overview of existing and multiplicity of degree theory and propose pivoting methods and iterative methods for degree analysis, including sensitivity and stability analysis.
Journal ArticleDOI
Numerical Methods for Nonlinear Variational Problems
Roland Glowinski,J. T. Oden +1 more