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Reduced basis method for the adapted mesh and Monte Carlo methods applied to an elliptic stochastic problem. (English) Zbl 1438.65275

Summary: In this paper, we consider a stochastic elliptic partial differential system and we aim to approximate the solution using the Monte Carlo method based on the finite elements method. To speed up the resolution and reduce the CPU time of computation, we propose to couple the reduced basis method with the adapted mesh method based on an a posteriori error estimate. Balancing the discretization and the Monte Carlo errors is very important to avoid performing an excessive number of iterations. Numerical experiments show and confirm the efficiency of our proposed algorithm.

MSC:

65N15 Error bounds for boundary value problems involving PDEs
35J20 Variational methods for second-order elliptic equations
65C05 Monte Carlo methods
35B45 A priori estimates in context of PDEs
35R60 PDEs with randomness, stochastic partial differential equations
65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs

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References:

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