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arXiv · 2007.04147

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

Gregory Etangsale·Marwan Fahs·Vincent Fontaine·Nalitiana Rajaonison
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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 $\mathcal{O}(1/h^{1+\delta})$, where $h$ denotes the mesh size and $\delta$ is a user-dependent parameter. We then quantify its direct impact on the convergence analysis, namely, the (strong) consistency, discrete coercivity, and boundedness (with $h^{\delta}$-dependency), and we derive updated error estimates for both discrete energy- and $L^{2}$-norms. The originality of the error analysis relies specifically on the use of conforming interpolants of the exact solution. All theoretical results are supported by numerical evidence.

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Gregory Etangsale, Marwan Fahs, Vincent Fontaine, Nalitiana Rajaonison. 2020-07-08. Improved error estimates of hybridizable interior penalty methods using a variable penalty for highly anisotropic diffusion problems. https://arxiv.org/abs/2007.04147

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