Convergence analysis for spectral approximation to a scalar transport equation with a random wave speed

Tao Zhou*, Tao TANG

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)643-656
Number of pages14
JournalJournal of Computational Mathematics
Volume30
Issue number6
DOIs
Publication statusPublished - Nov 2012

Scopus Subject Areas

  • Computational Mathematics

User-Defined Keywords

  • Analytic regularity
  • Scalar transport equations
  • Spectral convergence
  • Stochastic collocation
  • Stochastic Galerkin

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