Local Analysis of the Fully Discrete Local Discontinuous Galerkin Method for the Time-Dependent Singularly Perturbed Problem
Year: 2017
Author: Yao Cheng, Qiang Zhang
Journal of Computational Mathematics, Vol. 35 (2017), Iss. 3 : pp. 265–288
Abstract
In this paper we consider the fully discrete local discontinuous Galerkin method, where the third order explicit Runge-Kutta time marching is coupled. For the one-dimensional time-dependent singularly perturbed problem with a boundary layer, we shall prove that the resulted scheme is not only of good behavior at the local stability, but also has the double-optimal local error estimate. It is to say, the convergence rate is optimal in both space and time, and the width of the cut-off subdomain is also nearly optimal, if the boundary condition at each intermediate stage is given in a proper way. Numerical experiments are also given.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.1605-m2015-0398
Journal of Computational Mathematics, Vol. 35 (2017), Iss. 3 : pp. 265–288
Published online: 2017-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 24
Keywords: Local analysis Runge-Kutta method Local discontinuous Galerkin method Singularly perturbed problem Boundary layer.
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