High-Order Spectral Stochastic Finite Element Analysis of Stochastic Elliptical Partial Differential Equations

Galerkin Finite Element Approximations of Stochastic Elliptic Partial Differential Equations

We describe and analyze two numerical methods for a linear elliptic problem with stochastic coefficients and homogeneous Dirichlet boundary conditions. Here the aim of the computations is to approximate statistical moments of the solution, and, in particular, we give a priori error estimates for the computation of the expected value of the solution. The first method generates independent identi...

Finite element methods for semilinear elliptic stochastic partial differential equations

We study finite element methods for semilinear stochastic partial differential equations. Error estimates are established. Numerical examples are also presented to examine our theoretical results. Mathematics Subject Classification (2000) 65N30 · 65N15 · 65C30 · 60H15

An eXtended Stochastic Finite Element Method for solving stochastic partial differential equations on random domains

Recently, a new strategy was proposed to solve stochastic partial differential equations on random domains. It is based on the extension to the stochastic framework of the eXtended Finite Element Method (X-FEM). This method leads by a “direct” calculus to an explicit solution in terms of the variables describing the randomness on the geometry. It relies on two major points: the implicit represe...

Stochastic Partial Differential Equations

Computational Method for Fractional-Order Stochastic Delay Differential Equations

Dynamic systems in many branches of science and industry are often perturbed by various types of environmental noise. Analysis of this class of models are very popular among researchers. In this paper, we present a method for approximating solution of fractional-order stochastic delay differential equations driven by Brownian motion. The fractional derivatives are considered in the Caputo sense...