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.

翻译：本文针对二阶椭圆型方程提出了一种带有内部项过罚的富集Galerkin方法变体。具有内部过罚的双线性形式产生了一种非标准范数，这与经典间断Galerkin方法中的离散能量范数不同。然而，我们证明通过结合先验和后验误差分析技术，可以基于标准离散能量范数获得最优先验误差估计。我们还通过分析双线性形式的谱等价性，表明内部过罚对于构造对网格细化具有鲁棒性的预条件器具有优势。文中包含数值结果以说明收敛性和预条件结果。