A robust discontinuous Galerkin method for solving convection-diffusion problems

In this paper, a new DG method was designed to solve the model problem of the one-dimensional singularly-perturbed convection-diffusion equation. With some special chosen numerical traces, the existence and uniqueness of the DG solution is provided. The superconvergent points inside each element are...

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Bibliographic Details
Published in:Acta Mathematicae Applicatae Sinica 2008-07, Vol.24 (3), p.483-496
Main Authors: Zhang, Zuo-zheng, Xie, Zi-qing, Tao, Xia
Format: Article
Language:English
Subjects:
Applications of Mathematics
Math Applications in Computer Science
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Theoretical
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Summary:In this paper, a new DG method was designed to solve the model problem of the one-dimensional singularly-perturbed convection-diffusion equation. With some special chosen numerical traces, the existence and uniqueness of the DG solution is provided. The superconvergent points inside each element are observed. Particularly, the 2 p + 1-order superconvergence and even uniform superconvergence under layer-adapted mesh are observed numerically.
ISSN:0168-9673
1618-3932
DOI:10.1007/s10255-008-8036-7