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, in order to guarantee well-posedness, are well known. 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.

翻译：混合有限元方法用于求解以鞍点形式表述的各类椭圆型偏微分方程的理论已建立数十年之久。该主题主要研究定义于同一乘积空间（包含主变量-乘子的形状对与测试对）上的变分公式。当这些空间或涉及乘子的两个双线性形式存在差异时，鞍点问题即为非对称的。为确保问题适定性，该领域文献所规定的乘积空间需满足的三个inf-sup条件已广为人知。然而，现有文献中关于此类问题逼近方法的论述仍有改进与阐明空间。在简要回顾现有贡献以佐证上述论断后，本文针对求解非对称鞍点问题的主变量-乘子对建立了更精细的全局误差界。除适定性条件外，我们指出前述inf-sup条件中的三个常数是确定其中稳定常数所需的全部要素，并给出了该稳定常数的显式表达式。作为补充，我们还分别给出了仅依赖于这三个常数的两个未知量的精细化误差界。