SIAM Journal on Numerical Analysis, Volume 61, Issue 6, Page 2940-2966, December 2023.
Abstract. The discontinuous Galerkin approximation of the grad-div and curl-curl problems formulated in conservative first-order form is investigated. It is shown that the approximation is spectrally correct, thereby confirming numerical observations made by various authors in the literature. This result hinges on the existence of discrete involutions which are formulated as discrete orthogonality properties. The involutions are crucial to establish discrete versions of weak Poincaré–Steklov inequalities that hold true at the continuous level.

中文翻译：

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一阶形式的 Grad-Div 和 Curl-Curl 算子的间断伽辽金近似是保合且谱正确的

《SIAM 数值分析杂志》，第 61 卷，第 6 期，第 2940-2966 页，2023 年 12 月。
摘要。研究了以保守一阶形式表述的 grad-div 和curl-curl 问题的不连续伽辽金近似。结果表明，该近似值在光谱上是正确的，从而证实了文献中不同作者所做的数值观察。该结果取决于离散对合的存在，离散对合被表述为离散正交性属性。对合对于建立在连续水平上成立的弱庞加莱-斯特克洛夫不等式的离散版本至关重要。