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 norms obtained by Nečas and on the general framework of -convergence theory.
Keywords: numerical methods, non-conforming approximations, $\Gamma $-convergence
@article{COCV_2008__14_4_802_0,
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},
year = {2008},
publisher = {EDP Sciences},
volume = {14},
number = {4},
doi = {10.1051/cocv:2008011},
mrnumber = {2451798},
zbl = {1154.65054},
language = {en},
url = {https://www.numdam.org/articles/10.1051/cocv:2008011/}
}
TY - JOUR
AU - Davini, Cesare
AU - Paroni, Roberto
TI - External approximation of first order variational problems via $W^{-1, p}$ estimates
JO - ESAIM: Control, Optimisation and Calculus of Variations
PY - 2008
SP - 802
EP - 824
VL - 14
IS - 4
PB - EDP Sciences
UR - https://www.numdam.org/articles/10.1051/cocv:2008011/
DO - 10.1051/cocv:2008011
LA - en
ID - COCV_2008__14_4_802_0
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%A Paroni, Roberto
%T External approximation of first order variational problems via $W^{-1, p}$ estimates
%J ESAIM: Control, Optimisation and Calculus of Variations
%D 2008
%P 802-824
%V 14
%N 4
%I EDP Sciences
%U https://www.numdam.org/articles/10.1051/cocv:2008011/
%R 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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