We provide a systematic way to design computable bilinear forms which, on the class of subspaces $W^* \subseteq \mathcal{V}'$ that can be obtained by duality from a given finite dimensional subspace $W$ of an Hilbert space $\mathcal{V}$, are spectrally equivalent to the scalar product of $\mathcal{V}'$. Such a bilinear form can be used to build a stabilized discretization algorithm for the solution of an abstract saddle point problem allowing to decouple, in the choice of the discretization spaces, the requirements related to the approximation from the inf-sup compatibility condition, which, as we show, can not be completely avoided.
翻译：我们提供了一种系统的方法来设计可比较的双线形式。在子空间的等级上,这些可计算双线形式($W ⁇ \ subseteq \ mathcal{V}}$),可以通过一个特定的有限维次空间的双重性从一个特定的有限维次空间获得,W$W$Hilbert 空间$\mathcal{V}$),在光谱上相当于$\ mathcal{V}$的标量产值。这种双线形式可以用来构建一种稳定的离散算法,解决一个抽象的支撑点问题,从而在选择离散空间时,能够分辨出与近距离相匹配条件相关的要求,正如我们所显示的那样,这不可能完全避免。
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