Polynomial preserving recovery of an over-penalizedsymmetric interior penalty Galerkin method for elliptic problems

Lunji Song; Zhimin Zhang

doi:10.3934/dcdsb.2015.20.1405

Article Contents

2015, Volume 20, Issue 5: 1405-1426. Doi: 10.3934/dcdsb.2015.20.1405

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Polynomial preserving recovery of an over-penalized symmetric interior penalty Galerkin method for elliptic problems

Lunji Song^1, and
Zhimin Zhang^2,

1.
School of Mathematics and Statistics, and Key Laboratory of Applied Mathematics and Complex Systems in Gansu Province, Lanzhou University, Lanzhou 730000
2.
Beijing Computational Science Research Center, Beijing 100094

Received: February 2014

Revised: January 2015

Published: July 2015

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Abstract

A polynomial preserving recovery technique is applied to an over-penalized symmetric interior penalty method. The discontinuous Galerkin solution values are used to recover the gradient and to further construct an a posteriori error estimator in the energy norm. In addition, for uniform triangular meshes and mildly structured meshes satisfying the $\epsilon$-$\sigma$ condition, the method for the linear element is superconvergent under the regular pattern and under the chevron pattern, while it is superconvergent for the quadratic element under the regular pattern.

Keywords:

Symmetric interior penalty Galerkin method,
PPR,
discrete least-squares fitting,
superconvergence,
a posteriori error estimator.

Mathematics Subject Classification: Primary: 65N15, 65N30, 97N50.

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