External approximation of first order variational problems via W-1,p estimates

Cesare Davini; Roberto Paroni

ESAIM: Control, Optimisation and Calculus of Variations (2008)

  • Volume: 14, Issue: 4, page 802-824
  • ISSN: 1292-8119

Abstract

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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.

How to cite

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Davini, Cesare, and Paroni, Roberto. "External approximation of first order variational problems via W-1,p estimates." ESAIM: Control, Optimisation and Calculus of Variations 14.4 (2008): 802-824. <http://eudml.org/doc/250314>.

@article{Davini2008,
abstract = { 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. },
author = {Davini, Cesare, Paroni, Roberto},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Numerical methods; non-conforming approximations; Γ-convergence; -convergence; estimates; discontinuous Galerkin method; Necas reverse inequality; convergence; discretized functionals},
language = {eng},
month = {1},
number = {4},
pages = {802-824},
publisher = {EDP Sciences},
title = {External approximation of first order variational problems via W-1,p estimates},
url = {http://eudml.org/doc/250314},
volume = {14},
year = {2008},
}

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
DA - 2008/1//
PB - EDP Sciences
VL - 14
IS - 4
SP - 802
EP - 824
AB - 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.
LA - eng
KW - Numerical methods; non-conforming approximations; Γ-convergence; -convergence; estimates; discontinuous Galerkin method; Necas reverse inequality; convergence; discretized functionals
UR - http://eudml.org/doc/250314
ER -

References

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