Stochastic Spectral Formulations for Elliptic Problems

Sylvain Maire () and Etienne Tanré ()
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Sylvain Maire: Université de Toulon et du Var, ISITV

A chapter in Monte Carlo and Quasi-Monte Carlo Methods 2008, 2009, pp 513-528 from Springer

Abstract: 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.

Keywords: Elliptic Problem; Euler Scheme; Simulation Scheme; Quantization Point; Sphere Method (search for similar items in EconPapers)
Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-04107-5_33

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DOI: 10.1007/978-3-642-04107-5_33

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