In this Note we discuss the numerical solution of a two-dimensional, fully nonlinear elliptic equation of the Pucci's type, completed by Dirichlet boundary conditions. The solution method relies on a least-squares formulation taking place in a subset of , where Q is the space of the symmetric tensor-valued functions with components in . After an appropriate space discretization the resulting finite dimensional problem is solved by an iterative method operating alternatively in the spaces and approximating and Q, respectively. The results of numerical experiments are presented; they validate the methodology discussed in this Note.
Dans cette Note, on étudie la résolution numérique d'une équation elliptique bi-dimensionelle, pleinement non linéaire et de type Pucci. La méthode de résolution repose sur une formulation par moindres carrés dans un sous-ensemble de où Q est l'espace des fonctions à valeurs tensorielles symetriques , dont les composantes sont dans . Après approximation par éléments finis, on résoud le problème en dimension finie qui en résulte par une méthode itérative qui opère alternativement dans les espaces et , approximations respectives de et Q. Les résultats d'expériences numériques sont presentés ; ils valident la méthodologie numérique décrite dans cette Note.
Accepted:
Published online:
Edward J. Dean 1; Roland Glowinski 1, 2
@article{CRMATH_2005__341_6_375_0, author = {Edward J. Dean and Roland Glowinski}, title = {On the numerical solution of a two-dimensional {Pucci's} equation with {Dirichlet} boundary conditions: a least-squares approach}, journal = {Comptes Rendus. Math\'ematique}, pages = {375--380}, publisher = {Elsevier}, volume = {341}, number = {6}, year = {2005}, doi = {10.1016/j.crma.2005.08.002}, language = {en}, }
TY - JOUR AU - Edward J. Dean AU - Roland Glowinski TI - On the numerical solution of a two-dimensional Pucci's equation with Dirichlet boundary conditions: a least-squares approach JO - Comptes Rendus. Mathématique PY - 2005 SP - 375 EP - 380 VL - 341 IS - 6 PB - Elsevier DO - 10.1016/j.crma.2005.08.002 LA - en ID - CRMATH_2005__341_6_375_0 ER -
%0 Journal Article %A Edward J. Dean %A Roland Glowinski %T On the numerical solution of a two-dimensional Pucci's equation with Dirichlet boundary conditions: a least-squares approach %J Comptes Rendus. Mathématique %D 2005 %P 375-380 %V 341 %N 6 %I Elsevier %R 10.1016/j.crma.2005.08.002 %G en %F CRMATH_2005__341_6_375_0
Edward J. Dean; Roland Glowinski. On the numerical solution of a two-dimensional Pucci's equation with Dirichlet boundary conditions: a least-squares approach. Comptes Rendus. Mathématique, Volume 341 (2005) no. 6, pp. 375-380. doi : 10.1016/j.crma.2005.08.002. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2005.08.002/
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