TY - JOUR T1 - Convergence Analysis for Spectral Approximation to a Scalar Transport Equation with a Random Wave Speed 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 -
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.