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Zbl 0907.65147
Allen, E.J.; Novosel, S.J.; Zhang, Z.
Finite element and difference approximation of some linear stochastic partial differential equations. (English)
[J] Stochastics Stochastics Rep. 64, No.1-2, 117-142 (1998). ISSN 1045-1129; ISSN 1029-0346/e

A linear elliptic differential equation with additive white noise and a linear parabolic equation with space and time white noise are considered. The solutions are defined by integral equations which contain the free function. If the noise processes are approximated by piecewise constant random processes then the solutions of the above stochastic equations have more regularity and approximate the solutions of the original problems. The approximating equations are solved by difference and finite element methods. Convergence rates are given. Numerical experiments show that the finite element methods are computationally more efficient.
[W.Grecksch (Halle)]

MSC 2000:: *65C99 Numerical simulation
35R60 PDE with randomness
35J25 Second order elliptic equations, boundary value problems
35K15 Second order parabolic equations, initial value problems
60H15 Stochastic partial differential equations
65N06 Finite difference methods (BVP of PDE)
65N12 Stability and convergence of numerical methods (BVP of PDE)
65N30 Finite numerical methods (BVP of PDE)
65M06 Finite difference methods (IVP of PDE)
65M12 Stability and convergence of numerical methods (IVP of PDE)
65M60 Finite numerical methods (IVP of PDE)

Keywords: stochastic partial differential equation; finite elements; differences methods; linear elliptic equation; convergence; numerical experiments

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