Mathematical Modelling and Computer Simulation

[摘要] This article adopts and analyzes a stochastic collocation method to approximate the solution of four order elliptic partial differential equations with random coefficients and forcing terms, which are applied for some mathematicalbiology model. The method is composed of a Galerkin finite approximation in space and a collocation in the zeros of suitable tensor product orthogonal polynomials (Gauss points) in the probability space, and natural brings on the solution of uncoupled deterministic problems. The well-posedness of the elliptic partial differential equations is investigated as well under some regular assumptions. Strong error estimates for the fully discrete solution using L2 norms are obtained in this work.

[关键词] Collocation techniques;Galerkin finite element methods;Stochastic PDEs;Smolyak approximation