We summarize some general ideas regarding approximation of mixed variational problems using saddle point reformulation. We consider the concepts of optimal and almost optimal (or $\alpha$) test norm and provide estimates for the continuity and stability constants. A preconditioning strategy for solving the discrete mixed formulations is used in combination with the special test norms. We further provide a choice for a discrete trial space, that depends on the choice of a standard test space and leads to discrete stability, when using the appropriate test norm. Examples to illustrate how the stability of the saddle point discretization can be improved using special test norms are included.

我们总结了一些有关使用鞍点重构近似混合变分问题的一般思路。我们考虑最优和几乎最优的概念（或$\alpha$）测试规范，并提供连续性和稳定性常数的估算值。结合特殊测试规范使用了用于解决离散混合配方的预处理策略。当使用适当的测试规范时，我们进一步为离散的试验空间提供了选择，这取决于对标准测试空间的选择并导致离散的稳定性。提供了一些示例，以说明如何使用特殊的测试规范来改善鞍点离散化的稳定性。