Galerkin Methods for Stochastic Partial Differential Equations with Multiplicative Noise

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Mirsajadi, Hora-Sadat | 2017

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 50374 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Zohouri-Zangeneh, Bijan
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 examples
Keywords:
Stochastic Partial Differential Equation ; Finite Element Method ; Multiplicative Noise ; Galerkin Method in the Spectrum Domain ; Lipschitz Nonlinearities ; Optimal Error Estimates ; Spatio-Temparal Discretization