In this work, ideas previously introduced for a discontinuous Galerkin recovery method in one dimension, that involves a penalty stabilization term, are extended to an elliptic differential equation in several dimensions and different types of boundary conditions and meshes. Using standard arguments for other existing discontinuous Galerkin methods, we show results of existence and uniqueness of the solution. Also, optimal convergence rates are proved theoretically and confirmed numerically. Likewise, the numerical experiments allow us to analyze of the effect of the stabilization parameter.

中文翻译：

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具有扩散问题的稳定化的不连续Galerkin恢复方案

在这项工作中，先前针对一维不连续Galerkin恢复方法引入的想法（涉及惩罚稳定项）被扩展为多个维度以及边界条件和网格的不同类型的椭圆微分方程。使用其他现有不连续Galerkin方法的标准参数，我们展示了该解决方案存在性和唯一性的结果。此外，最佳收敛速度在理论上得到了证明，并在数值上得到了证实。同样，数值实验使我们能够分析稳定参数的影响。