Communications in Mathematical Sciences

Volume 10 (2012)

Number 4

The effect of finite element discretization on the stationary distribution of SPDEs

Pages: 1143 – 1159

DOI: http://dx.doi.org/10.4310/CMS.2012.v10.n4.a6

Author

Jochen Voss (School of Mathematics, University of Leeds, United Kingdom)

Abstract

This article studies the effect of discretization error on the stationary distribution of stochastic partial differential equations (SPDEs). We restrict the analysis to the effect of space discretization performed by finite element schemes. The main result is that under appropriate assumptions the stationary distribution of the finite element discretization converges in total variation norm to the stationary distribution of the full SPDE.

Keywords

SPDEs, finite element discretization, stationary distribution

2010 Mathematics Subject Classification

60H15, 60H35, 65C30

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