Superconvergent discontinuous Galerkin methods for linear non-selfadjoint and indefinite elliptic problems
type: Item
instance of: scholarly article
title: Superconvergent discontinuous Galerkin methods for linear non-selfadjoint and indefinite elliptic problems
zbMATH Open document ID: 1272.65085
author: Sangita Yadav
author: Neela Nataraj
author: Amiya K. Pani
published in: Journal of Scientific Computing
publication date: 2013-02-04T00:00:00Z
review text: The article deals with a superconvergent discontinuous Galerkin method for the following linear non-selfadjoint and indefinite elliptic problem \[ -\nabla \cdot (a(x)\nabla u(x)+ b(x)u)+c(x)u(x)=f(x) \; \text{in} \; \Omega, \] \[ u(x)=0 \; \text{on} \; \partial \Omega. \] The main result of the paper is the estimate \[ \|u-u_h\|+{\| q- q_h\|}+\|\sigma-\sigma_h\| \leq C h^{k+1}, \] where \(q=\nabla u\), \(\sigma=a q \), and the triplet \(u_h, q_h, \sigma_h\) stands for the approximation of \(u\), \(q\), \(\sigma\) by the discontinuous Galerkin method when piecewise polynomials of degree \(k\) are used. With a suitable post-processing \(u^*_{h}\) of \(u_h\) it is shown that \[ \|u-u_h^*\|\leq Ch^{k+2}. \] The article is concluded with numerical examples which confirm the theoretical results.
reviewed by: Iwan Gawriljuk
Mathematics Subject Classification ID: 65N12
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 65N15
Mathematics Subject Classification ID: 35J25
zbMATH DE Number: 6134441
zbMATH Keywords: non-selfadjoint and indefinite linear elliptic problems
zbMATH Keywords: superconvergence
zbMATH Keywords: discontinuous Galerkin method
zbMATH Keywords: optimal error estimate
zbMATH Keywords: post-processing solution
zbMATH Keywords: numerical examples
MaRDI profile type: Publication
full work available at URL: s10915-012-9601-z
OpenAlex ID: W1996586630
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DOI: 10.1007/S10915-012-9601-Z
description: scientific article; zbMATH DE number 6134441