The aim of this Note is to present a quasi-optimal a priori error estimate for the linear finite element approximation of the so-called two-dimensional Signorini problem, i.e. the equilibrium of a plane linearly elastic body in contact with a rigid foundation. Previous works on that subject give either non-optimal estimates or with a more restrictive supplementary condition on the solution.
On présente dans cette Note une estimation optimale de lʼerreur dʼapproximation par éléments finis affines du problème de Signorini, cʼest à dire du problème de lʼéquilibre dʼun corps élastique en contact avec une fondation rigide. Les travaux précédents sur ce sujet donnent soit des résultats non optimaux, soit avec des conditions supplémentaires plus contraignantes sur la solution.
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Yves Renard 1
@article{CRMATH_2012__350_5-6_325_0, author = {Yves Renard}, title = {A quasi-optimal a priori error estimate for the two-dimensional {Signorini} problem approximated by linear finite elements}, journal = {Comptes Rendus. Math\'ematique}, pages = {325--328}, publisher = {Elsevier}, volume = {350}, number = {5-6}, year = {2012}, doi = {10.1016/j.crma.2012.01.024}, language = {en}, }
TY - JOUR AU - Yves Renard TI - A quasi-optimal a priori error estimate for the two-dimensional Signorini problem approximated by linear finite elements JO - Comptes Rendus. Mathématique PY - 2012 SP - 325 EP - 328 VL - 350 IS - 5-6 PB - Elsevier DO - 10.1016/j.crma.2012.01.024 LA - en ID - CRMATH_2012__350_5-6_325_0 ER -
%0 Journal Article %A Yves Renard %T A quasi-optimal a priori error estimate for the two-dimensional Signorini problem approximated by linear finite elements %J Comptes Rendus. Mathématique %D 2012 %P 325-328 %V 350 %N 5-6 %I Elsevier %R 10.1016/j.crma.2012.01.024 %G en %F CRMATH_2012__350_5-6_325_0
Yves Renard. A quasi-optimal a priori error estimate for the two-dimensional Signorini problem approximated by linear finite elements. Comptes Rendus. Mathématique, Volume 350 (2012) no. 5-6, pp. 325-328. doi : 10.1016/j.crma.2012.01.024. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2012.01.024/
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