Weak convergence for a spatial approximation of the nonlinear stochastic heat equation
Journal article, 2016

We find the weak rate of convergence of the spatially semidiscrete finite element approximation of the nonlinear stochastic heat equation. Both multiplicative and additive noise is considered under different assumptions. This extends an earlier result of Debussche in which time discretization is considered for the stochastic heat equation perturbed by white noise. It is known that this equation has a solution only in one space dimension. In order to obtain results for higher dimensions, colored noise is considered here, besides white noise in one dimension. Integration by parts in the Malliavin sense is used in the proof. The rate of weak convergence is, as expected, essentially twice the rate of strong convergence.

finite element

Malliavin calculus

error estimate

Nonlinear stochastic heat equation

weak convergence

multiplicative noise



Adam Andersson

Chalmers, Mathematical Sciences, Mathematics

University of Gothenburg

Stig Larsson

University of Gothenburg

Chalmers, Mathematical Sciences, Mathematics

Mathematics of Computation

0025-5718 (ISSN) 1088-6842 (eISSN)

Vol. 85 299 1335-1358

Subject Categories

Computational Mathematics

Probability Theory and Statistics


Basic sciences



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