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Frontiers of Mathematics in China

, Volume 8, Issue 4, pp 825–836 | Cite as

Time discontinuous Galerkin space-time finite element method for nonlinear Sobolev equations

  • Siriguleng He
  • Hong LiEmail author
  • Yang Liu
Research Article

Abstract

This article presents a complete discretization of a nonlinear Sobolev equation using space-time discontinuous Galerkin method that is discontinuous in time and continuous in space. The scheme is formulated by introducing the equivalent integral equation of the primal equation. The proposed scheme does not explicitly include the jump terms in time, which represent the discontinuity characteristics of approximate solution. And then the complexity of the theoretical analysis is reduced. The existence and uniqueness of the approximate solution and the stability of the scheme are proved. The optimalorder error estimates in L 2(H 1) and L 2(L 2) norms are derived. These estimates are valid under weak restrictions on the space-time mesh, namely, without the condition k n ch 2, which is necessary in traditional space-time discontinuous Galerkin methods. Numerical experiments are presented to verify the theoretical results.

Keywords

Nonlinear Sobolev equation time discontinuous Galerkin spacetime finite element method optimal error estimate 

MSC

65M12 65M60 

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Copyright information

© Higher Education Press and Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.School of Mathematical SciencesInner Mongolia UniversityHohhotChina

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