Nodal Superconvergence of the Local Discontinuous Galerkin Method for Singularly Perturbed Problems

Document Type

Article

Publication Date

3-1-2018

Department

Mathematics

School

Mathematics and Natural Sciences

Abstract

In this paper, a superconvergence of order (lnN∕N)2k+1" role="presentation" style="box-sizing: border-box; display: inline-block; line-height: normal; font-size: 14.4px; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">(lnN∕N)2k+1 for the numerical traces of the LDG approximation to a one dimensional singularly perturbed convection–diffusion–reaction problem is proved. The LDG method is applied on a Shishkin mesh with 2N" role="presentation" style="box-sizing: border-box; display: inline-block; line-height: normal; font-size: 14.4px; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">2N elements, and we use polynomials of degree at most k" role="presentation" style="box-sizing: border-box; display: inline-block; line-height: normal; font-size: 14.4px; word-spacing: normal; word-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">k on each element. This result puts the numerical finding reported in Xie and Zhang (2007), Xie et al. (2009) on firm mathematical ground.

Publication Title

Journal of Computational and Applied Mathematics

Volume

330

First Page

95

Last Page

116

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