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arXiv · 2208.09969

Interior over-penalized enriched Galerkin methods for second order elliptic equations

Jeonghun J. Lee·Omar Ghattas
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Abstract

In this paper we propose a variant of enriched Galerkin methods for second order elliptic equations with over-penalization of interior jump terms. The bilinear form with interior over-penalization gives a non-standard norm which is different from the discrete energy norm in the classical discontinuous Galerkin methods. Nonetheless we prove that optimal a priori error estimates with the standard discrete energy norm can be obtained by combining a priori and a posteriori error analysis techniques. We also show that the interior over-penalization is advantageous for constructing preconditioners robust to mesh refinement by analyzing spectral equivalence of bilinear forms. Numerical results are included to illustrate the convergence and preconditioning results.

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Jeonghun J. Lee, Omar Ghattas. 2022-08-21. Interior over-penalized enriched Galerkin methods for second order elliptic equations. https://arxiv.org/abs/2208.09969

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