Related papers: Finite Element Approximations of Stochastic Linear…
A standard finite element method discretizes the stochastic linear Schr\"{o}dinger equation driven by additive noise in the spatial variables. The weak convergence of the resulting approximate solution is analyzed, and it is established…
In this article, we analyze semi-discrete finite element approximation and full discretization of a fourth-order stochastic pseudo-parabolic equation in a bounded convex polygonal domain driven by additive Wiener noise. We use the finite…
In this article, we have analyzed the full discretization of the Stochastic semilinear Schr\"{o}dinger equation in a bounded convex polygonal domain driven by multiplicative Wiener noise. We use the finite element method for spatial…
We propose and analyse a new type of fully discrete finite element approximation of a class of linear stochastic parabolic evolution equations with additive noise. Our discretization differs from previous ones in that we use a finite…
This paper aims to investigate the numerical approximation of a general second order parabolic stochastic partial differential equation(SPDE) driven by multiplicative and additive noise. Our main interest is on such SPDEs where the…
We consider the stochastic Cahn-Hilliard equation driven by additive Gaussian noise in a convex domain with polygonal boundary in dimension $d\le 3$. We discretize the equation using a standard finite element method in space and a fully…
This paper aims to investigate the numerical approximation of semilinear non-autonomous stochastic partial differential equations (SPDEs) driven by multiplicative or additive noise. Such equations are more realistic than autonomous SPDEs…
In this paper the numerical solution of non-autonomous semilinear stochastic evolution equations driven by an additive Wiener noise is investigated. We introduce a novel fully discrete numerical approximation that combines a standard…
We propose and analyse a new type of fully discrete surface finite element approximation of a class of linear parabolic stochastic evolution equations with additive noise. Our discretization uses a surface finite element approximation of…
A fully discrete approximation of the semi-linear stochastic wave equation driven by multiplicative noise is presented. A standard linear finite element approximation is used in space and a stochastic trigonometric method for the temporal…
Numerical approximation of a stochastic partial integro-differential equation driven by a space- time white noise is studied by truncating a series representation of the noise, with finite element method for spatial discretization and…
This paper deals with the backward Euler method applied to semilinear parabolic stochastic partial differential equations (SPDEs) driven by additive noise. The SPDE is discretized in space by the finite element method and in time by the…
This paper aims to investigate the numerical approximation of a general second order parabolic stochastic partial differential equation(SPDE) driven by multiplicative and additive noise under more relaxed conditions. The SPDE is discretized…
We consider the numerical approximation of the mild solution to a semilinear stochastic wave equation driven by additive noise. For the spatial approximation we consider a standard finite element method and for the temporal approximation, a…
A numerical analysis for the fully discrete approximation of an operator Lyapunov equation related to linear SPDEs (stochastic partial differential equations) driven by multiplicative noise is considered. The discretization of the Lyapunov…
In this paper, we consider a semi-linear stochastic strongly damped wave equation driven by additive Gaussian noise. Following a semigroup framework, we establish existence, uniqueness and space-time regularity of a mild solution to such…
In this paper, we consider the numerical approximation of a general second order semilinear stochastic partial differential equation (SPDE) driven by multiplicative and additive noise. Our main interest is on such SPDEs where the nonlinear…
We consider an initial- and Dirichlet boundary- value problem for a fourth-order linear stochastic parabolic equation, in two or three space dimensions, forced by an additive space-time white noise. Discretizing the space-time white noise a…
Efficient simulation of stochastic partial differential equations (SPDE) on general domains requires noise discretization. This paper employs piecewise linear interpolation of noise in a fully discrete finite element approximation of a…
A fully discrete approximation of the linear stochastic wave equation driven by additive noise is presented. A standard finite element method is used for the spatial discretisation and a stochastic trigonometric scheme for the temporal…