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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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Pointwise error estimates of the local discontinuous Galerkin method for a second order elliptic problem
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by Hongsen Chen PDF
Math. Comp. 74 (2005), 1097-1116 Request permission

Abstract:

In this paper we derive some pointwise error estimates for the local discontinuous Galerkin (LDG) method for solving second-order elliptic problems in $R^N$ ($N\geq 2$). Our results show that the pointwise errors of both the vector and scalar approximations of the LDG method are of the same order as those obtained in the $L^2$ norm except for a logarithmic factor when the piecewise linear functions are used in the finite element spaces. Moreover, due to the weighted norms in the bounds, these pointwise error estimates indicate that when at least piecewise quadratic polynomials are used in the finite element spaces, the errors at any point $z$ depend very weakly on the true solution and its derivatives in the regions far away from $z$. These localized error estimates are similar to those obtained for the standard conforming finite element method.
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Additional Information
  • Hongsen Chen
  • Affiliation: Department of Mathematics, University of Wyoming, Laramie, Wyoming 82070
  • Email: hchen@uwyo.edu
  • Received by editor(s): December 7, 2003
  • Received by editor(s) in revised form: February 21, 2004
  • Published electronically: July 16, 2004
  • © Copyright 2004 American Mathematical Society
  • Journal: Math. Comp. 74 (2005), 1097-1116
  • MSC (2000): Primary 65N30, 65N15, 65N12; Secondary 41A25, 35B45, 35J20
  • DOI: https://doi.org/10.1090/S0025-5718-04-01700-4
  • MathSciNet review: 2136995