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

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


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