Communications in Mathematical Sciences
Volume 10 (2012)
The effect of finite element discretization on the stationary distribution of SPDEs
Pages: 1143 – 1159
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.
SPDEs, finite element discretization, stationary distribution
2010 Mathematics Subject Classification
60H15, 60H35, 65C30