Approximation of infima in the calculus of variations

The goal of this paper is to give numerical estimates for some problems of the Calculus of Variations in the nonhomogeneous scalar case. The stored energy function considered is then a function ϕ : Ω × Rn → R. We try to compare the infimum of the energy defined by ϕ on a Sobolev space, with the infimum of the same energy on a finite element space, in terms of the mesh size.