Document Type
Journal Article
Department/Unit
Department of Mathematics
Title
Convergence analysis for spectral approximation to a scalar transport equation with a random wave speed
Language
English
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. Copyright 2012 by AMSS, Chinese Academy of Sciences.
Keywords
Analytic regularity, Scalar transport equations, Spectral convergence, Stochastic collocation, Stochastic Galerkin
Publication Date
2012
Source Publication Title
Journal of Computational Mathematics
Volume
30
Issue
6
Start Page
643
End Page
656
Publisher
Global Science Press
DOI
10.4208/jcm.1206-m4012
Link to Publisher's Edition
http://dx.doi.org/10.4208/jcm.1206-m4012
ISSN (print)
02549409
ISSN (electronic)
19917139
APA Citation
Zhou, T., & Tang, T. (2012). Convergence analysis for spectral approximation to a scalar transport equation with a random wave speed. Journal of Computational Mathematics, 30 (6), 643-656. https://doi.org/10.4208/jcm.1206-m4012