Superconvergence of discontinuous Galerkin methods for hyperbolic systems

Authors:
Tie Zhang;Jiandong Li;Shuhua Zhang
Affiliations:
Department of Mathematics, School of Information Science and Engineering, Northeastern University, Shenyang 110004, China;Department of Mathematics, School of Information Science and Engineering, Northeastern University, Shenyang 110004, China;Department of Mathematics, Tianjin University of Finance and Economics, Tianjin 300222, China and Liu Hui Center for Applied Mathematics, Nankai University 300071, Tianjin University 300072, China
Venue:
Journal of Computational and Applied Mathematics
Year:
2009

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Abstract

In this paper, the discontinuous Galerkin method for the positive and symmetric, linear hyperbolic systems is constructed and analyzed by using bilinear finite elements on a rectangular domain, and an O(h^2)-order superconvergence error estimate is established under the conditions of almost uniform partition and the H^3-regularity for the exact solutions. The convergence analysis is based on some superclose estimates derived in this paper. Finally, as an application, the numerical treatment of Maxwell equation is discussed and computational results are presented.