SEMINAIRE D'ANALYSE NUMERIQUE
Année universitaire 2008-2009
Jeudi 15 janvier 2008 :
Stig LARSSON
(Chalmers, Suède)
Spatial approximation of the stochastic heat and wave equations by
finite elements.
We consider the linear stochastic heat and wave equations in several
spatial variables driven by additive correlated space-time noise. The
equations are written in the abstract form
du + A u dt = dW
where $A$ is the generator of a strongly continuous semigroup of
bounded linear operators on Hilbert space (analytic semigroup in the
case of the heat equation) and $W$ is a Hilbert space valued Wiener
process. The equation is discretized in the spatial variable by a
finite element method. We provide an abstract framework for the error
analysis and we prove strong convergence estimates, i.e., error
estimates in a mean square norm.