In this paper we prove a new abstract stability result for perturbed saddle-point problems based on a norm fitting technique. We derive the stability condition according to Babu\v{s}ka's theory from a small inf-sup condition, similar to the famous Ladyzhenskaya-Babu\v{s}ka-Brezzi (LBB) condition, and the other standard assumptions in Brezzi's theory, in a combined abstract norm. The construction suggests to form the latter from individual {\it fitted} norms that are composed from proper seminorms. This abstract framework not only allows for simpler (shorter) proofs of many stability results but also guides the design of parameter-robust norm-equivalent preconditioners. These benefits are demonstrated on mixed variational formulations of generalized Poisson, Stokes, vector Laplace and Biot's equations.

翻译：在本文中,我们证明了基于规范安装技术的受扰动马鞍问题的新抽象稳定结果。 我们根据Babu\v{s{s}ka的理论,从一个小的软质条件(类似于著名的Ladyzenskaya-Babu\v}s}ka-Brezzi(LBB)条件)和Brezzi理论中的其他标准假设(综合抽象规范)中得出了一个新的抽象稳定结果。 构建建议从由适当的准规范构成的个体(适合的)规范中形成后一种稳定结果。 这个抽象框架不仅允许对许多稳定性结果进行更简单的(短)证明,而且还指导参数-robust规范等同先决条件的设计。 这些好处表现在普瓦森、斯托克斯、矢量拉贝和生物等式的混合变式配方中。