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Some Remarks on Nonuniqueness of Minimizers for Discrete Minimization Problems
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M. Chipot
Published/Copyright:
June 7, 2010
Abstract
We investigate the issue of uniqueness and nonuniqueness of minimizers for the approximation of variational problems. We show that when the continuous problem does not admit a minimizer its approximation by finite elements may lead to several discrete minimizers.
Key words and phrases.: Approximation; non-convex; calculus of variations; minimizers; finite elements
Received: 2000-02-23
Revised: 2001-04-03
Published Online: 2010-06-07
Published in Print: 2001-December
© Heldermann Verlag
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- Asymptotic Behavior of Relatively Nonexpansive Operators in Banach Spaces
- Exceptional Sets for Universally Polygonally Approximable Functions
- Some Remarks on Nonuniqueness of Minimizers for Discrete Minimization Problems
- The Nevanlinna Theorem of the Classical Theory of Moments Revisited
- Measures in Locally Compact Groups are Carried by Meager Sets
- On Sequences of Upper and Lower Semi-Quasicontinuous Functions
- Compositions of Sierpiński-Zygmund Functions and Related Combinatorial Cardinals
- Gradient-Finite Element Method for Nonlinear Neumann Problems
- On Sets Determined by Sequences of Quasi-Continuous Functions
- On Minimal Pairwise Sufficient Statistics
Keywords for this article
Approximation;
non-convex;
calculus of variations;
minimizers;
finite elements
Articles in the same Issue
- Asymptotic Behavior of Relatively Nonexpansive Operators in Banach Spaces
- Exceptional Sets for Universally Polygonally Approximable Functions
- Some Remarks on Nonuniqueness of Minimizers for Discrete Minimization Problems
- The Nevanlinna Theorem of the Classical Theory of Moments Revisited
- Measures in Locally Compact Groups are Carried by Meager Sets
- On Sequences of Upper and Lower Semi-Quasicontinuous Functions
- Compositions of Sierpiński-Zygmund Functions and Related Combinatorial Cardinals
- Gradient-Finite Element Method for Nonlinear Neumann Problems
- On Sets Determined by Sequences of Quasi-Continuous Functions
- On Minimal Pairwise Sufficient Statistics
