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Improved Error estimates of hybridizable interior penalty methods using a variable penalty for highly anisotropic diffusion problems

Abstract : In this paper, we derive improved a priori error estimates for families of hybridizable interior penalty discontinuous Galerkin (H-IP) methods using a variable penalty for second-order elliptic problems. The strategy is to use a penalization function of the form O(1/h^{1+δ}), where h denotes the mesh size and δ is a user-dependent parameter. We then quantify its direct impact on the convergence analysis, namely, the (strong) consistency, discrete coercivity and boundedness (with h δ-dependency), and we derive updated error estimates for both discrete energy-and L^2-norms. All theoretical results are supported by numerical evidence.
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Preprints, Working Papers, ...
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https://hal.archives-ouvertes.fr/hal-02893064
Contributor : Vincent Fontaine <>
Submitted on : Sunday, June 20, 2021 - 6:28:08 AM
Last modification on : Wednesday, June 30, 2021 - 9:40:13 PM

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2007.04147.pdf
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  • HAL Id : hal-02893064, version 2
  • ARXIV : 2007.04147

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Grégory Etangsale, Marwan Fahs, Vincent Fontaine, Nalitiana Rajaonison. Improved Error estimates of hybridizable interior penalty methods using a variable penalty for highly anisotropic diffusion problems. 2020. ⟨hal-02893064v2⟩

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