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Stochastic Spectral Formulations for Elliptic Problems

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Monte Carlo and Quasi-Monte Carlo Methods 2008

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 quantized or not.

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Author information

Authors and Affiliations

  1. ISITV, Université de Toulon et du Var, avenue G. Pompidou, BP 56, 83262, La Valette du Var, France

    Sylvain Maire

Authors
  1. Sylvain Maire
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  2. Etienne Tanré
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Correspondence to Sylvain Maire .

Editor information

Editors and Affiliations

  1. Centre de Recherches Mathématiques, Université de Montréal, Montreal, H3C 3J7, Canada

    Pierre L' Ecuyer

  2. Dept. Statistics, Stanford University, Serra Mall 390, Stanford, 94305-4065, U.S.A.

    Art B. Owen

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Maire, S., Tanré, E. (2009). Stochastic Spectral Formulations for Elliptic Problems. In: L' Ecuyer, P., Owen, A. (eds) Monte Carlo and Quasi-Monte Carlo Methods 2008. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04107-5_33

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