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Energy estimates for Lagrange finite elements. (English) Zbl 0902.65024
The goal of this paper is to expose some techniques developed to obtain numerical estimates in problems of calculus of variations lacking of convexity. Lagrange finite elements for families of regular triangulations are considered. Estimates of the infimum corresponding to the discretized problem are obtained in terms of mesh size. Simple examples from nonlinear elasticity are discussed.
Reviewer: V.Arnăutu (Iaşi)

65K10 Numerical optimization and variational techniques
74B20 Nonlinear elasticity
49J20 Existence theories for optimal control problems involving partial differential equations
49M15 Newton-type methods
74S05 Finite element methods applied to problems in solid mechanics
74S30 Other numerical methods in solid mechanics (MSC2010)
74P10 Optimization of other properties in solid mechanics