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Journal of Scientific Computing

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01-01-2013

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

Authors: Sangita Yadav, Amiya K. Pani, Neela Nataraj

Published in: Journal of Scientific Computing | Issue 1/2013

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Abstract

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 k≥1 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.

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Title: Superconvergent Discontinuous Galerkin Methods for Linear Non-selfadjoint and Indefinite Elliptic Problems
Authors: Sangita Yadav
Amiya K. Pani
Neela Nataraj
Publication date: 01-01-2013
Publisher: Springer US
Published in: Journal of Scientific Computing / Issue 1/2013
Print ISSN: 0885-7474
Electronic ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-012-9601-z

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