Stochastic Partial Differential Equations with Multiplicative Noise - Numerical simulations of strong and weak approximation errors
Sammanfattning
A finite element Galerkin spatial discretization together with a backward Euler
scheme is implemented to simulate strong error rates of the homogeneous stochastic
heat equation with multiplicative trace class noise in one dimension. For the noise,
two different operators displaying different degrees of regularity are considered, one
of which is of Nemytskii type. The discretization scheme is extended to include discretization
of the covariance operator of the Q-Wiener process driving the equation.
The results agree with the theory. Furthermore, for exploratory reasons, weak error
rates are also simulated using the classical Monte Carlo method and the multilevel
Monte Carlo method.
Examinationsnivå
Student essay