External approximation of first order variational problems via $W^{-1,p}$ estimates

Davini, Cesare; Paroni, Roberto

ESAIM: Control, Optimisation and Calculus of Variations, Tome 14 (2008) no. 4, pp. 802-824.

Here we present an approximation method for a rather broad class of first order variational problems in spaces of piece-wise constant functions over triangulations of the base domain. The convergence of the method is based on an inequality involving $W^{-1,p}$ norms obtained by Nečas and on the general framework of $\Gamma$-convergence theory.

Classification : 65N12, 65N30, 46N10, 74K20, 74S05
Mots clés : numerical methods, non-conforming approximations, $\Gamma $-convergence

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