Weak convergence of the backward Euler method for stochastic Cahn–Hilliard equation with additive noise

Rate of Weak Convergence of the Finite Element Method for the Stochastic Heat Equation with Additive Noise

The stochastic heat equation driven by additive noise is discretized in the spatial variables by a standard finite element method. The weak convergence of the approximate solution is investigated and the rate of weak convergence is found to be twice that of strong convergence.

Weak exponential schemes for stochastic differential equations with additive noise

This paper develops weak exponential schemes for the numerical solution of stochastic differential equations (SDEs) with additive noise. In particular, this work provides first and second-order methods which use at each iteration the product of the exponential of the Jacobian of the drift term with a vector. The article also addresses the rate of convergence of the new schemes. Moreover, numeri...

Weak Convergence of Finite Element Approximations of Linear Stochastic Evolution Equations with Additive Noise

A unified approach is given for the analysis of the weak error of spatially semidiscrete finite element methods for linear stochastic partial differential equations driven by additive noise. An error representation formula is found in an abstract setting based on the semigroup formulation of stochastic evolution equations. This is then applied to the stochastic heat, linearized Cahn-Hilliard, a...

Convergence Estimates for a Linear Backward Euler Scheme for the Saturation Equation

In a previous work, stability and consistency results were established for a linearized Euler scheme for the saturation equation. In this paper we continue the mathematical analysis of the scheme, in preparation for its numerical treatment in a future work. We use the regularity results, obtained previously, to establish error estimates in L ( ) for the linear scheme. This work is done with the...

The finite element method for a linear stochastic parabolic partial differential equation driven by additive noise