abstract:
We consider the numerical approximation of solutions of the
stochastic, Hilbert space valued heat equation
\begin{equation}
dX_t+AX_tdt=Q^{1/2}dW_t\qquad\forall{t}\in(0,T)\;\mbox{and}\;{X}_0\in{H},
\end{equation}
with an elliptic operator $A:D(A)\rightarrow H$, and
$Q:H\rightarrow{H}$ is the covariance operator of the driving Wiener
process. We apply different domain decomposition algorithms based on
explicit and implicit time stepping, paired with finite element and
backward Euler discretisation to solve the problem, and give optimal
strong and weak rates of convergence. |