Convergence Analysis for Spectral Approximation to a Scalar Transport Equation with a Random Wave Speed
Year: 2012
Journal of Computational Mathematics, Vol. 30 (2012), Iss. 6 : pp. 643–656
Abstract
This paper is concerned with the initial-boundary value problems of scalar transport equations with uncertain transport velocities. It was demonstrated in our earlier works that regularity of the exact solutions in the random spaces (or the parametric spaces) can be determined by the given data. In turn, these regularity results are crucial to convergence analysis for high order numerical methods. In this work, we will prove the spectral convergence of the stochastic Galerkin and collocation methods under some regularity results or assumptions. As our primary goal is to investigate the errors introduced by discretizations in the random space, the errors for solving the corresponding deterministic problems will be neglected.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.1206-m4012
Journal of Computational Mathematics, Vol. 30 (2012), Iss. 6 : pp. 643–656
Published online: 2012-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 14
Keywords: Scalar transport equations Analytic regularity Stochastic Galerkin Stochastic collocation Spectral convergence.