Wick-stochastic finite element solution of reaction-diffusion problems

Authors:
Hassan Manouzi;Mohammed Seaıd;Mostafa Zahri
Affiliations:
Departement de Mathematiques et Statistique, Universite Laval, Quebec, Canada;Fachbereich Mathematik, TU Darmstadt, 64289 Darmstadt, Germany;Fachbereich Mathematik, Johann Wolfgang Goethe-Universität, 60054 Frankfurt am Main, Germany
Venue:
Journal of Computational and Applied Mathematics
Year:
2007

Citing 4
Cited 4

BI-CGSTAB: a fast and smoothly converging variant of BI-CG for the solution of nonsymmetric linear systems

SIAM Journal on Scientific and Statistical Computing
Stochastic simulation of coupled reaction-diffusion processes

Journal of Computational Physics
Stochastic partial differential equations: a modeling, white noise functional approach

Stochastic partial differential equations: a modeling, white noise functional approach
Numerical Approximation of Some Linear Stochastic Partial Differential Equations Driven by Special Additive Noises

SIAM Journal on Numerical Analysis

A Spectral Stochastic Semi-Lagrangian Method for Convection-Diffusion Equations with Uncertainty

Journal of Scientific Computing
Solving Wick-stochastic water waves using a Galerkin finite element method

Mathematics and Computers in Simulation
Numerical simulation of stochastic replicator models in catalyzed RNA-like polymers

Mathematics and Computers in Simulation
A finite volume method for scalar conservation laws with stochastic time-space dependent flux functions

Journal of Computational and Applied Mathematics

Quantified Score

Hi-index	7.29

Visualization

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-Ito 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.