An implementation of a stochastic partial differential equation in FEniCS
Typ
Examensarbete för masterexamen
Program
Publicerad
2019
Författare
IÑIGUEZ ORDOÑEZ, MARIO
Modellbyggare
Tidskriftstitel
ISSN
Volymtitel
Utgivare
Sammanfattning
Computational platforms based on intuitive and efficient software can allow for
a easy and accessible computational mathematical modelling. FEniCS is an opensource
software that allows for automated way of implementing finite element method(FEM)
code for partial differential equations from the variational formulation of a differential
equation. Using the FEniCS platform we implement the Poisson equation with
variable coefficients
r · (a(x)ru(x)) = f(x).
The noise term is chosen as a = exp(T) where T is a Gaussian random field modelled
as a solution to a stochastic differential equation of the form
(− ) /2T = W 2 N.
where W. This equation was solved using fractional approximation of the operator
and a finite element discretisation. For both equations a thorough step-by-step
implementation is presented with the aforementioned equation being completely
implemented in FEniCS. As a measure of quality of implementation a strong mean
square error was estimated. The convergence rate of the strong error results for
the Gaussian random field is compared to the theoretical results. The result of our
implementation quality, confirms the theory.