Discontinuous Galerkin methods for elliptic partial differential equations with random coefficients. (English) Zbl 1290.65006
The numerical solution of elliptic equations with random coefficients with zero boundary condition on the boundary of a polygonal domain is studied, where the randomness comes from a bounded random vector \(y\) with density function \( \rho\). A discontinuous Galerkin method and a discontinuous Galerkin Monte Carlo method are performed and their convergence are obtained, respectively. Numerical examples are examined.
Reviewer: Gong Guanglu (Beijing)
MSC:
| 65C30 | Numerical solutions to stochastic differential and integral equations |
| 65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
| 65N15 | Error bounds for boundary value problems involving PDEs |
| 65C05 | Monte Carlo methods |
| 60H15 | Stochastic partial differential equations (aspects of stochastic analysis) |
| 60H35 | Computational methods for stochastic equations (aspects of stochastic analysis) |
| 35R60 | PDEs with randomness, stochastic partial differential equations |
| 65N12 | Stability and convergence of numerical methods for boundary value problems involving PDEs |
Keywords:
stochastic discontinuous Galerkin method; finite noise; stochastic elliptic equation; Monte carlo simulation; a priori error estimate; numerical exampleReferences:
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