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Application of generalized Gauss-Radau projections for the local discontinuous Galerkin method for linear convection-diffusion equations


Authors: Yao Cheng, Xiong Meng and Qiang Zhang
Journal: Math. Comp. 86 (2017), 1233-1267
MSC (2010): Primary 65M12, 65M15, 65M60
DOI: https://doi.org/10.1090/mcom/3141
Published electronically: September 1, 2016
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Abstract: In this paper we consider the local discontinuous Galerkin method based on the generalized alternating numerical fluxes for solving the linear convection-diffusion equations in one dimension and two dimensions. As an application of generalized Gauss-Radau projections, we get rid of the dual argument and obtain directly the optimal $ L^2$-norm error estimate in a uniform framework. The sharpness of the theoretical results is demonstrated by numerical experiments.


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Additional Information

Yao Cheng
Affiliation: Department of Mathematics, Nanjing University, Nanjing 210093, Jiangsu Province, People’s Republic of China
Email: ycheng@smail.nju.edu.cn

Xiong Meng
Affiliation: Department of Mathematics, Harbin Institute of Technology, Harbin 150001, Heilongjiang Province, People’s Republic of China
Email: xiongmeng@hit.edu.cn

Qiang Zhang
Affiliation: Department of Mathematics, Nanjing University, Nanjing 210093, Jiangsu Province, People’s Republic of China
Email: qzh@nju.edu.cn

DOI: https://doi.org/10.1090/mcom/3141
Keywords: Local discontinuous Galerkin method, convection-diffusion equation, error estimates, generalized Gauss--Radau projection
Received by editor(s): June 6, 2015
Received by editor(s) in revised form: October 28, 2015
Published electronically: September 1, 2016
Additional Notes: The research of the first author was supported by NSFC grant 11271187 and the program B for outstanding PhD candidate of Nanjing University.
The research of the second author was supported by PIRS of HIT grant B201404 and NSFC grant 11501149. Additional support was provided by the EU under the 7th Framework Programme Marie Curie International Incoming Fellowships FP7-PEOPLE-2013-IIF, GA number 622845 while the author was in residence at University of East Anglia, United Kingdom
The research of the third author was supported by NSFC grants 11271187 and 11571290
Article copyright: © Copyright 2016 American Mathematical Society