Stochastic Finite Element Technique For Solving A Class Of SDE

Abstract

Dans ce mémoire, nous avons présenté la méthode des éléments finis stochastiques , où nous avons abordé les aspects les plus importants des processus stochastiques communs et aussi la théorie de Lax-Milgram dans le ntionné les méthodes stochastiques les plus importantes pour résoudre les équations différentielles stochastiques, méthode de Monte Carlo, méthode de quadrature, méthode de perturbation, où nous avons appliqué this memory, we presented the method of elements finite stochastic, where we touched on the most important common stochastic processes and also the theory of Lax-Milgram in the deterministic element finite method to prove the existence and uniqueness of the solution. We also mentioned the most important stochastic methods for solving stochastic differential equations ( Monte Carlo method, quadrature method, perturbation method), where we applied some of them in mechanics, especially in geo-techniques and fracture mechanics.certaines des en mécanique, notamment en géotechniques et en mécanique de la rupture.In this memory, we presented the method of elements finite stochastic, where we touched on the most important common stochastic processes and also the theory of Lax-Milgram in the deterministic element finite method to prove the existence and uniqueness of the solution. We also mentioned the most important stochastic methods for solving stochastic differential equations ( Monte Carlo method, quadrature method, perturbation method), where we applied some of them in mechanics, especially in geo-techniques and fracture mechanics.