Optimal error estimates of the local discontinuous Galerkin method for surface diffusion of graphs on Cartesian meshes

Liangyue Ji, Yan Xu

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4 Scopus citations

Abstract

In (Xu and Shu in J. Sci. Comput. 40:375-390, 2009), a local discontinuous Galerkin (LDG) method for the surface diffusion of graphs was developed and a rigorous proof for its energy stability was given. Numerical simulation results showed the optimal order of accuracy. In this subsequent paper, we concentrate on analyzing a priori error estimates of the LDG method for the surface diffusion of graphs. The main achievement is the derivation of the optimal convergence rate k+1 in the L 2 norm in one-dimension as well as in multi-dimensions for Cartesian meshes using a completely discontinuous piecewise polynomial space with degree k≥1.

Original languageEnglish (US)
Pages (from-to)1-27
Number of pages27
JournalJournal of Scientific Computing
Volume51
Issue number1
DOIs
StatePublished - Apr 2012

Bibliographical note

Funding Information:
Research of Y. Xu was supported by NSFC grant No. 10971211, No. 11031007, FANEDD No. 200916, FANEDD of CAS, NCET No. 09-0922 and the Fundamental Research Funds for the Central Universities.

Copyright:
Copyright 2012 Elsevier B.V., All rights reserved.

Keywords

  • Error estimates
  • Local discontinuous Galerkin method
  • Stability
  • Surface diffusion of graphs

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