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arXiv · 1911.12298

A priori and a posteriori error analysis of an unfitted HDG method for semi-linear elliptic problems

Nestor Sánchez·Tonatiuh Sánchez-Vizuet·Manuel E. Solano
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Abstract

We present a priori and a posteriori error analysis of a high order hybridizable discontinuous Galerkin (HDG) method applied to a semi-linear elliptic problem posed on a piecewise curved, non polygonal domain. We approximate $\Omega$ by a polygonal subdomain $\Omega_h$ and propose an HDG discretization, which is shown to be optimal under mild assumptions related to the non-linear source term and the distance between the boundaries of the polygonal subdomain $\Omega_h$ and the true domain $\Omega$. Moreover, a local non-linear post-processing of the scalar unknown is proposed and shown to provide an additional order of convergence. A reliable and locally efficient a posteriori error estimator that takes into account the error in the approximation of the boundary data of $\Omega_h$ is also provided.

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Nestor Sánchez, Tonatiuh Sánchez-Vizuet, Manuel E. Solano. 2019-11-27. A priori and a posteriori error analysis of an unfitted HDG method for semi-linear elliptic problems. https://arxiv.org/abs/1911.12298

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