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Superconvergence of bi-k Degree Time-Space Fully Discontinuous Finite Element for First-Order Hyperbolic Equations

Published online by Cambridge University Press:  28 May 2015

Hongling Hu  and
Chuanmiao Chen
Hongling Hu
Affiliation:
College of Mathematics and Computer Science, Key Laboratory of High Performance Computing and Stochastic Information Processing, Hunan Normal University, Changsha 410081, China
Chuanmiao Chen*
Affiliation:
College of Mathematics and Computer Science, Key Laboratory of High Performance Computing and Stochastic Information Processing, Hunan Normal University, Changsha 410081, China
*
*Corresponding author. Email: hhling625@163.com (H. L. Hu), cmchen@hunnu.edu.cn (C. M. Chen)
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Abstract

In this paper, we present a superconvergence result for the bi-k degree time-space fully discontinuous finite element of first-order hyperbolic problems. Based on the element orthogonality analysis (EOA), we first obtain the optimal convergence order of discontinuous Galerkin finite element solution. Then we use orthogonality correction technique to prove a superconvergence result at right Radau points, which is higher one order than the optimal convergence rate. Finally, numerical results are presented to illustrate the theoretical analysis.

Keywords

65M6035L0465M12Superconvergencehyperbolic equationfinite elementdiscontinuous Galerkin methodRadau points
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 7 , Issue 3 , June 2015 , pp. 323 - 337
Copyright
Copyright © Global-Science Press 2015 

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