We propose a uniform block diagonal preconditioner for the condensed $H$(div)-conforming HDG scheme of a parameter-dependent saddle point problem that includes the generalized Stokes problem and linear elasticity. An optimal preconditioner is obtained for the stiffness matrix for the velocity/displacement block via auxiliary space preconditioning (ASP) technique. A robust preconditioner spectrally equivalent to the Schur complement of element-piecewise constant pressure space is also constructed. Finally, numerical results of generalized Stokes and steady linear elasticity equations verify the robustness of our proposed preconditioner with respect to mesh size, Lam\'e parameters and time step size.

翻译：我们提出一个统一的区块对立先决条件,用于一个以参数为依存的马鞍问题(包括普遍的斯托克斯问题和线性弹性)的凝结(HDG)(div)符合HDG(cronced $H$)(div)的办法,该办法包含一个以参数为依存的马鞍问题,其中包括普遍的斯托克斯问题和线性弹性;通过辅助空间先决条件(ASP)技术,为速度/残疾区块的僵硬性矩阵获得一个最佳先决条件;另外,还建造了一个强大的光谱先决条件,相当于Schur对元素单向不变压力空间的补充。最后,普遍的斯托克斯和稳定的线性弹性方程式的数值结果证实了我们所提议的先决条件在网状尺寸、Lam\e参数和时间步骤大小方面的坚固性。