TY - JOUR
T1 - Convergence Analysis for Spectral Approximation to a Scalar Transport Equation with a Random Wave Speed
AU - Tao Zhou & Tao Tang
JO - Journal of Computational Mathematics
VL - 6
SP - 643
EP - 656
PY - 2012
DA - 2012/12
SN - 30
DO - http://doi.org/10.4208/jcm.1206-m4012
UR - https://global-sci.org/intro/article_detail/jcm/8457.html
KW - Scalar transport equations, Analytic regularity, Stochastic Galerkin, Stochastic
collocation, Spectral convergence.
AB - <p style="text-align: justify;">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.</p>