Simulation of stochastic partial differential equations using finite element methods

These notes describe numerical issues that may arise when implementing a simulation method for a stochastic partial differential equation (SPDE). It is shown that an additional approximation of the noise does not necessarily affect the order of convergence of a discretization method for a SPDE driven by Lévy noise. Furthermore, finite element methods are explicitly given and simulations are done. In statistical tests, it is shown that the simulations obey the theoretical orders of convergence.