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Superconvergent Discontinuous Galerkin Methods for Linear Non-selfadjoint and Indefinite Elliptic Problems

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Title Superconvergent Discontinuous Galerkin Methods for Linear Non-selfadjoint and Indefinite Elliptic Problems
 
Creator YADAV, S
PANI, AK
NATARAJ, N
 
Subject Superconvergent DG methods
Non-selfadjoint and indefinite linear elliptic problems
Optimal error estimate
Post-processed solution
Superconvergence results
Numerical experiments
 
Description Based on Cockburn et al. (Math. Comp. 78:1-24, 2009), superconvergent discontinuous Galerkin methods are identified for linear non-selfadjoint and indefinite elliptic problems. With the help of an auxiliary problem which is the discrete version of a linear non-selfadjoint elliptic problem in divergence form, optimal error estimates of order k+1 in L (2)-norm for the potential and the flux are derived, when piecewise polynomials of degree ka parts per thousand yen1 are used to approximate both potential and flux variables. Using a suitable post-processing of the discrete potential, it is then shown that the resulting post-processed potential converges with order k+2 in L (2)-norm. The article is concluded with a numerical experiment which confirms the theoretical results.
 
Publisher SPRINGER/PLENUM PUBLISHERS
 
Date 2014-10-14T12:32:44Z
2014-10-14T12:32:44Z
2013
 
Type Article
 
Identifier JOURNAL OF SCIENTIFIC COMPUTING, 54(1)45-76
http://dx.doi.org/10.1007/s10915-012-9601-z
http://dspace.library.iitb.ac.in/jspui/handle/100/14428
 
Language en