Wick-stochastic finite element solution of reaction–diffusion problems |
| |
Authors: | Hassan Manouzi,Mohammed Seaı¨ d,Mostafa Zahri |
| |
Affiliation: | 1. Departement de Mathematiques et Statistique, Universite Laval, Quebec, Canada;2. Fachbereich Mathematik, TU Darmstadt, 64289 Darmstadt, Germany;3. Fachbereich Mathematik, Johann Wolfgang Goethe-Universität, 60054 Frankfurt am Main, Germany |
| |
Abstract: | Real life reaction–diffusion problems are characterized by their inherent or externally induced uncertainties in the design parameters. This paper presents a finite element solution of reaction–diffusion equations of Wick type. Using the Wick-product properties and the Wiener–Itô chaos expansion, the stochastic variational problem is reformulated to a set of deterministic variational problems. To obtain the chaos coefficients in the corresponding deterministic reaction–diffusion, we implement the usual Galerkin finite element method using standard techniques. Once this representation is computed, the statistics of the numerical solution can be easily evaluated. Computational results are shown for one- and two-dimensional test examples. |
| |
Keywords: | 60H40 35K57 78M10 65M60 60H35 |
本文献已被 ScienceDirect 等数据库收录! |
|