In this paper we propose a variant of enriched Galerkin methods for second order elliptic equations with over-stabilization of interior jump terms. The bilinear form with interior over-stabilization 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-stabilization 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.

翻译：本文针对二阶椭圆方程提出了一种带有内跳项过稳定的富集Galerkin变体方法。具有内过稳定的双线性形式定义了一种非标准范数，该范数不同于经典间断Galerkin方法中的离散能量范数。然而，通过结合先验和后验误差分析技术，我们证明了仍可在标准离散能量范数下获得最优先验误差估计。同时，通过分析双线性形式的谱等价性，我们表明内过稳定有利于构建对网格细化具有鲁棒性的预处理子。文中包含数值结果以验证收敛性与预处理效果。