Simulation of stochastic partial differential equations using finite element methods

Abstract

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.

Keywords:

• finite element method
• stochastic partial differential equation
• Lévy process
• Galerkin's method

AMS Subject Classification::

• 60G60
• 60H15
• 60H35
• 65C30

Acknowledgements

The authors wish to express many thanks to Pao-Liu Chow, José-Luis Menaldi and Jürgen Potthoff for fruitful discussions and helpful comments.

Notes

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