Numerical methods for stochastic partial differential equations with multiple scales

Numerical methods for stochastic partial differential equations with multiple scales

A new method for solving numerically stochastic partial differential equations (SPDEs) with multiple scales is presented. The method combines a spectral method with the heterogeneous multiscale method (HMM) presented in [W. E, D. Liu, and E. Vanden-Eijnden, Comm. Pure Appl. Math., 58(11):1544–1585, 2005]. The class of problems that we consider are SPDEs with quadratic nonlinearities that were s...

Numerical methods for stochastic partial differential equations with multiples scales

Article history: Received 23 May 2011 Received in revised form 3 October 2011 Accepted 27 November 2011 Available online 13 December 2011

Partial Differential Equations with Numerical Methods

Numerical Methods for Partial Differential Equations

Robust Numerical Methods for Partial Differential Equations

The general theme of this project is to study numerical methods for systems of partial diffential equations which depend on one or more critical parameters. Typically, we are interested in systems which change type as a critical perturbation parameter tend to zero. Our goal is to construct numerical methods with convergence properties which are uniform with respect to the perturbation parameter...