External approximation of first order variational problems via ${W}^{-1,p}$ estimates
ESAIM: Control, Optimisation and Calculus of Variations, Volume 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.

DOI: 10.1051/cocv:2008011
Classification: 65N12,  65N30,  46N10,  74K20,  74S05
Keywords: numerical methods, non-conforming approximations, $\Gamma$-convergence
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author = {Davini, Cesare and Paroni, Roberto},
title = {External approximation of first order variational problems via $W^{-1, p}$ estimates},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {802--824},
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Davini, Cesare; Paroni, Roberto. External approximation of first order variational problems via $W^{-1, p}$ estimates. ESAIM: Control, Optimisation and Calculus of Variations, Volume 14 (2008) no. 4, pp. 802-824. doi : 10.1051/cocv:2008011. http://www.numdam.org/articles/10.1051/cocv:2008011/

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