Galerkin Methods for Stochastic Partial Differential Equations with Multiplicative Noise, M.Sc. Thesis Sharif University of Technology ; Zohouri-Zangeneh, Bijan (Supervisor)
Abstract
In this thesis we study Galerkin methods for semilinear stochastic partial differential equations (SPDEs) with multiplicative noise and Lipschitz continuous nonlinearities. The strong error of convergence for spatially semidiscrete approximations as well as a spatio-temporal discretization which is based on a linear implicit Euler–Maruyama method, are also investigated. We see that the obtained error estimates in both cases as well as the regularity results for the mild solution of the SPDE are optimal. The results hold for different Galerkin methods such as the standard finite element method or spectral Galerkin. At the end, these theoretical findings are accompanied by several numerical...
Cataloging briefGalerkin Methods for Stochastic Partial Differential Equations with Multiplicative Noise, M.Sc. Thesis Sharif University of Technology ; Zohouri-Zangeneh, Bijan (Supervisor)
Abstract
In this thesis we study Galerkin methods for semilinear stochastic partial differential equations (SPDEs) with multiplicative noise and Lipschitz continuous nonlinearities. The strong error of convergence for spatially semidiscrete approximations as well as a spatio-temporal discretization which is based on a linear implicit Euler–Maruyama method, are also investigated. We see that the obtained error estimates in both cases as well as the regularity results for the mild solution of the SPDE are optimal. The results hold for different Galerkin methods such as the standard finite element method or spectral Galerkin. At the end, these theoretical findings are accompanied by several numerical...
Find in contentBookmark
|
|