Department of Mathematics
Convergence analysis for spectral approximation to a scalar transport equation with a random wave speed
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.
Analytic regularity, Scalar transport equations, Spectral convergence, Stochastic collocation, Stochastic Galerkin
Source Publication Title
Journal of Computational Mathematics
Global Science Press
Zhou, Tao, and Tao Tang. "Convergence analysis for spectral approximation to a scalar transport equation with a random wave speed." Journal of Computational Mathematics 30.6 (2012): 643-656.