Numerical solutions of SPDEs with boundary noise
Galerkin finite element method is a technique for approximating solutions to stochastic partial differential equations (SPDEs) that has been extensively studied in the literature. In this thesis, we extend the scheme to solve the case where noise enters through the boundary of the domain. We prove that the optimal convergence rate is achieved for semi-linear parabolic SPDEs with random Neumann boundary conditions. Considering the advection-diffusion equation with boundary noise, we show that...[Show more]
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