The theory of mixed finite element methods for solving different types of elliptic partial differential equations in saddle point formulation is well established since many decades. This topic was mostly studied for variational formulations defined upon the same product spaces of both shape- and test-pairs of primal variable-multiplier. Whenever either these spaces or the two bilinear forms involving the multiplier are distinct, the saddle point problem is asymmetric. The three inf-sup conditions to be satisfied by the product spaces stipulated in work on the subject, to guarantee well-posedness, are known [(see, e.g., Exercise 2.14 of Ern and Guermond (Theory and practice of finite elements, Applied mathematical, sciences, Springer, 2004)]. However, the material encountered in the literature addressing the approximation of this class of problems left room for improvement and clarifications. After making a brief review of the existing contributions to the topic that justifies such an assertion, in this paper we set up finer global error bounds for the pair primal variable-multiplier solving an asymmetric saddle point problem. Besides well-posedness, the three constants in the aforementioned inf-sup conditions are identified as all that is needed for determining the stability constant appearing therein, whose expression is exhibited. As a complement, refined error bounds depending only on these three constants are given for both unknowns separately.

用于求解鞍点公式中不同类型的椭圆偏微分方程的混合有限元方法的理论在几十年前就已经很成熟了。该主题主要研究在原始变量乘子的形状对和测试对的相同乘积空间上定义的变分公式。每当这些空间或涉及乘数的两个双线性形式不同时，鞍点问题就是不对称的。为了保证适定性，该主题的工作中规定的乘积空间要满足的三个 inf-sup 条件是已知的[（参见 Ern 和 Guermond 的练习 2.14（有限元理论与实践，应用数学，科学，Springer，2004）]。然而，解决此类问题的近似的文献中遇到的材料留下了改进和澄清的空间。在简要回顾了证明这一断言的主题的现有贡献之后，在本文中，我们为求解非对称鞍点问题的原始变量乘子对设置了更精细的全局误差界。除了适定性之外，上述 inf-sup 条件中的三个常数被确定为确定稳定性所需的全部内容作为补充，分别为两个未知数给出了仅依赖于这三个常数的精确误差范围。