Treffer: Wick-stochastic finite element solution of reaction-diffusion problems
Title:
Wick-stochastic finite element solution of reaction-diffusion problems
Authors:
Source:
The first Indo-German Conference on PDE, Scientific Computing and Optimization in ApplicationsJournal of computational and applied mathematics. 203(2):516-532
Publisher Information:
Amsterdam: Elsevier, 2007.
Publication Year:
2007
Physical Description:
print, 16 ref
Original Material:
INIST-CNRS
Subject Terms:
Computer science, Informatique, Mathematics, Mathématiques, Sciences exactes et technologie, Exact sciences and technology, Sciences et techniques communes, Sciences and techniques of general use, Mathematiques, Mathematics, Combinatoire. Structures ordonnées, Combinatorics. Ordered structures, Combinatoire, Combinatorics, Plans d'expériences et configurations, Designs and configurations, Analyse mathématique, Mathematical analysis, Equations aux dérivées partielles, Partial differential equations, Calcul des variations et contrôle optimal, Calculus of variations and optimal control, Analyse numérique. Calcul scientifique, Numerical analysis. Scientific computation, Analyse numérique, Numerical analysis, Probabilités et statistiques numériques, Numerical methods in probability and statistics, Analyse numérique, Numerical analysis, Análisis numérico, Bruit blanc, White noise, Ruido blanco, Calcul 2 dimensions, Two-dimensional calculations, Chaos, Caos, Coefficient, Coeficiente, Conception, Design, Diseño, Diffusion, Difusión, Elément fini, Finite element, Elemento finito, Equation diffusion, Diffusion equation, Ecuación difusión, Equation différentielle, Differential equation, Ecuación diferencial, Equation dérivée partielle, Partial differential equation, Ecuación derivada parcial, Equation intégrale, Integral equation, Ecuación integral, Equation réaction diffusion, Reaction diffusion equation, Ecuación reacción difusión, Equation stochastique, Stochastic equation, Ecuación estocástica, Expansion, Expansión, Implémentation, Implementation, Implementación, Incertitude, Uncertainty, Incertidumbre, Mathématiques appliquées, Applied mathematics, Matemáticas aplicadas, Méthode Galerkin, Galerkin method, Método Galerkin, Méthode statistique, Statistical method, Método estadístico, Méthode élément fini, Finite element method, Método elemento finito, Norme, Standards, Norma, Plan expérience, Experimental design, Plan experiencia, Problème valeur initiale, Initial value problem, Problema valor inicial, Problème valeur limite, Boundary value problem, Problema valor limite, Représentation, Representation, Representación, Réaction, Reaction, Reacción, Simulation stochastique, Stochastic simulation, Simulación estocástica, Solution numérique, Numerical solution, Statistique, Statistics, Estadística, 05Bxx, 34XX, 35K57, 35XX, 49M15, 65C30, 65M99, 65Mxx, 65N99, 65Nxx, Problème diffusion, Problème variationnel, Variational problem, Produit Wick, Solution équation, 60H35, 60H40, 65M60, 78M10, Reaction-diffusion problems, Wick-stochastic partial differential equations
Document Type:
Konferenz
Conference Paper
File Description:
text
Language:
English
Author Affiliations:
Departement de Mathematiques et Statistique, Université Laval, Quebec, Canada
Fachbereich Mathematik, TU Darmstadt, 64289 Darmstadt, Germany
Fachbereich Mathematik, Johann Wolfgang Goethe -Universität, 60054 Frankfurt am Main, Germany
Fachbereich Mathematik, TU Darmstadt, 64289 Darmstadt, Germany
Fachbereich Mathematik, Johann Wolfgang Goethe -Universität, 60054 Frankfurt am Main, Germany
ISSN:
0377-0427
Rights:
Copyright 2007 INIST-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
Notes:
Mathematics
Accession Number:
edscal.18679401
Database:
PASCAL Archive
Weitere Informationen
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.