[Méthode des éléments finis pour une équation de Pucci à deux dimensions]
Cet article étudie une méthode d’éléments finis non linéaire des moindres carrés pour les solutions fortes du problème de la valeur limite de Dirichlet d’une équation de Pucci bidimensionnelle sur des domaines polygonaux convexes. Nous obtenons des estimations d’erreur a priori et a posteriori et présentons des résultats numériques corroborants, où les problèmes d’optimisation discrets non lisses et non linéaires sont résolus par une méthode d’ensemble active et une méthode de direction alternée avec multiplicateurs.
A nonlinear least-squares finite element method for strong solutions of the Dirichlet boundary value problem of a two-dimensional Pucci equation on convex polygonal domains is investigated in this paper. We obtain a priori and a posteriori error estimates and present corroborating numerical results, where the discrete nonsmooth and nonlinear optimization problems are solved by an active set method and an alternating direction method with multipliers.
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Mot clés : équation de Pucci, méthode des éléments finis, solution forte, estimations d’erreur a priori et a posteriori, moindres carrés non linéaires, méthode des ensembles actifs, ADMM
Susanne C. Brenner 1 ; Li-yeng Sung 1 ; Zhiyu Tan 2
@article{CRMECA_2023__351_S1_261_0, author = {Susanne C. Brenner and Li-yeng Sung and Zhiyu Tan}, title = {A finite element method for a two-dimensional {Pucci} equation}, journal = {Comptes Rendus. M\'ecanique}, pages = {261--276}, publisher = {Acad\'emie des sciences, Paris}, volume = {351}, number = {S1}, year = {2023}, doi = {10.5802/crmeca.224}, language = {en}, }
TY - JOUR AU - Susanne C. Brenner AU - Li-yeng Sung AU - Zhiyu Tan TI - A finite element method for a two-dimensional Pucci equation JO - Comptes Rendus. Mécanique PY - 2023 SP - 261 EP - 276 VL - 351 IS - S1 PB - Académie des sciences, Paris DO - 10.5802/crmeca.224 LA - en ID - CRMECA_2023__351_S1_261_0 ER -
Susanne C. Brenner; Li-yeng Sung; Zhiyu Tan. A finite element method for a two-dimensional Pucci equation. Comptes Rendus. Mécanique, Volume 351 (2023) no. S1, pp. 261-276. doi : 10.5802/crmeca.224. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.224/
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