Stochastic spectral formulations for elliptic problems

Sylvain Maire 1, 2 Etienne Tanré 1
1 TOSCA
INRIA Lorraine, CRISAM - Inria Sophia Antipolis - Méditerranée , UHP - Université Henri Poincaré - Nancy 1, Université Nancy 2, INPL - Institut National Polytechnique de Lorraine, CNRS - Centre National de la Recherche Scientifique : UMR7502
Abstract : We describe new stochastic spectral formulations with very good properties in terms of conditioning. These formulations are built by combining Monte Carlo approximations of the Feynman-Kac formula and standard deterministic approximations on basis functions. We give error bounds on the solutions obtained using these formulations in the case of linear approximations. Some numerical tests are made on an anisotropic diffusion equation using a tensor product Tchebychef polynomial basis and one random point schemes quantified or not.
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Sylvain Maire, Etienne Tanré. Stochastic spectral formulations for elliptic problems. L' Ecuyer, Pierre (ed.) and Owen, Art B. (ed.). Monte Carlo and quasi-Monte Carlo methods 2008. Proceedings of the 8th international conference Monte Carlo and quasi-Monte Carlo methods in scientific computing, Montréal, Canada, July 6--11, 2008., Berlin: Springer, pp.513--528, 2009, ⟨10.1007/978-3-642-04107-5_33⟩. ⟨inria-00340708⟩

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