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

This document is currently not available here.

Link to Publisher's Version

Share

COinS