Name
Abstract | ||
|---|---|---|
Mathematical requirements that the random coefficients of stochastic elliptical partial differential equations must satisfy such that they have unique solutions have been studied extensively. Yet, additional constraints that these coefficients must satisfy to provide realistic representations for physical quantities, referred to as physical requirements, have not been examined systematically. It is shown that current models for random coefficients constructed solely by mathematical considerations can violate physical constraints and, consequently, be of limited practical use. We develop alternative models for the random coefficients of stochastic differential equations that satisfy both mathematical and physical constraints. Theoretical arguments are presented to show potential limitations of current models and establish properties of the models developed in this study. Numerical examples are used to illustrate the construction of the proposed models, assess the performance of these models, and demonstrate the sensitivity of the solutions of stochastic differential equations to probabilistic characteristics of their random coefficients. |
Year | DOI | Venue |
|---|---|---|
2010 | 10.1016/j.jcp.2010.07.023 | J. Comput. Physics |
Keywords | Field | DocType |
physical quantity,stochastic elliptic partial differential equations,non-gaussian random functions,physical requirement,mathematical requirement,stochastic elliptical partial differential,probabilistic model,mathematical consideration,physical constraint,stochastic elliptic partial differential,karhunen–loéve/spectral expansions,current model,additional constraint,random coefficient,translation random functions,stochastic differential equation,parametric models,elliptic partial differential equation,satisfiability,random function,parametric model | Differential equation,Mathematical optimization,Mathematical analysis,Stochastic differential equation,Statistical model,Stochastic modelling,Probabilistic logic,Stochastic partial differential equation,Elliptic partial differential equation,Partial differential equation,Mathematics | Journal |
Volume | Issue | ISSN |
229 | 22 | Journal of Computational Physics |
Citations | PageRank | References |
3 | 0.42 | 4 |
Authors | ||
1 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Mircea Grigoriu | 1 | 4 | 3.83 |