Scientific Computing Group Report - Detail view

Identifier: 2011-3

Author(s): Y. Xu and C.-W. Shu

Title: Optimal error estimates of the semi-discrete local discontinuous Galerkin methods for high order wave equations

Page count: 32 pp.

Date: Jan. 27, 2011

Abstract:

In this paper, we introduce a general approach for proving optimal L2 error estimates for the semi-discrete local discontinuous Galerkin (LDG) methods solving linear high order wave equations. The optimal order of error estimates hold not only for the solution itself but also for the auxiliary variables in the LDG method approximating the various order derivatives of the solution. Several examples including the one-dimensional third order wave equation, one-dimensional fifth order wave equation, and multi-dimensional Shro ̈dinger equation are explored to demonstrate this approach. The main idea is to derive energy stability for the various auxiliary variables in the LDG discretization, via using the scheme and its time derivatives with different test functions. Special projections are utilized to eliminate the jump terms at the cell boundaries in the error estimate in order to achieve the optimal order of accuracy.

BibTeX:

@techreport{brown_sc_2011_3,
  title = "{Optimal error estimates of the semi-discrete local discontinuous Galerkin methods for high order wave equations}",
  author = "Y. Xu and C.-W. Shu",
  institution = "Scientific Computing Group, Brown University",
  number = "2011-3",
  address = "Providence, RI, USA",
  year = 2011,
  month = jan,
}

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