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Some remarks on nonuniqueness of minimizers for discrete minimization problems. (English) Zbl 1009.49026
The authors approximate the variational problem \[ \int\varphi(\nabla v(x)) dx\to \inf_{v\in W^{1,\infty}_0(\Omega)} \] by finite elements and show that when the continuous problem does not admit a minimizer its approximation may lead to several discrete minimizers.
MSC:
49M25 Discrete approximations in optimal control
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
49J10 Existence theories for free problems in two or more independent variables
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