Geodesic
External approximation of first order variational problems via W -1,p estimates
ESAIM: Control, Optimisation and Calculus of Variations, Tome 14 (2008) no. 4, pp. 802-824

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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 Γ-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},
     publisher = {EDP-Sciences},
     volume = {14},
     number = {4},
     year = {2008},
     doi = {10.1051/cocv:2008011},
     mrnumber = {2451798},
     zbl = {1154.65054},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv:2008011/}
}
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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, Tome 14 (2008) no. 4, pp. 802-824. doi: 10.1051/cocv:2008011

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