Year: 2013
International Journal of Numerical Analysis and Modeling, Vol. 10 (2013), Iss. 2 : pp. 350–373
Abstract
In this paper local discontinuous Galerkin method (LDG) was analyzed for solving 1-D convection-diffusion equations with a boundary layer near the outflow boundary. Local error estimates are established on quasi-uniform meshes with maximum mesh size $h$. On a subdomain with $O(h\ln(1/h))$ distance away from the outflow boundary, the $L^2$ error of the approximations to the solution and its derivative converges at the optimal rate $O(h^{k+1})$ when polynomials of degree at most $k$ are used. Numerical experiments illustrate that the rate of convergence is uniformly valid and sharp. The numerical comparison of the LDG method and the streamline-diffusion finite element method are also presented.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2013-IJNAM-572
International Journal of Numerical Analysis and Modeling, Vol. 10 (2013), Iss. 2 : pp. 350–373
Published online: 2013-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 24
Keywords: Local discontinuous Galerkin method singularly perturbed local error estimates.