Volume 30, Issue 6
Convergence Analysis for Spectral Approximation to a Scalar Transport Equation with a Random Wave Speed

Tao Zhou & Tao Tang

J. Comp. Math., 30 (2012), pp. 643-656

Published online: 2012-12

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  • 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.

  • Keywords

Scalar transport equations Analytic regularity Stochastic Galerkin Stochastic collocation Spectral convergence

  • AMS Subject Headings

52B10 65D18 68U05.

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-30-643, author = {Tao Zhou and Tao Tang}, title = {Convergence Analysis for Spectral Approximation to a Scalar Transport Equation with a Random Wave Speed}, journal = {Journal of Computational Mathematics}, year = {2012}, volume = {30}, number = {6}, pages = {643--656}, 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. }, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1206-m4012}, url = {http://global-sci.org/intro/article_detail/jcm/8457.html} }
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 KW - Analytic regularity KW - Stochastic Galerkin KW - Stochastic collocation KW - 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.
Tao Zhou & Tao Tang. (1970). Convergence Analysis for Spectral Approximation to a Scalar Transport Equation with a Random Wave Speed. Journal of Computational Mathematics. 30 (6). 643-656. doi:10.4208/jcm.1206-m4012
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