The auxiliary space preconditioning (ASP) technique is applied to the HDG schemes for three different elliptic problems with a parameter dependent low order term, namely, a symmetric interior penalty HDG scheme for the scalar reaction-diffusion equation, a divergence-conforming HDG scheme for a vectorial reaction-diffusion equation, and a C 0 -continuous interior penalty HDG scheme for the generalized biharmonic equation with a low order term. Uniform preconditioners are obtained for each case and the general ASP theory by J. Xu [21] is used to prove the optimality with respect to the mesh size and uniformity with respect to the low order parameter.

翻译：辅助空间先决条件(ASP)技术适用于HDG方案,涉及三个不同的外省问题,参数依次为低顺序,即:对称内置刑罚(对称内置刑罚)方案,用于卡拉反射反射方程式;对矢量反射反射方程式采用分立的HDG方案;对通用双调方程式采用C 0-连续内置刑罚(HDG)方案,低顺序期;对每个案件都采用统一的先决条件;J. Xu [21] 的ASP一般理论,用于证明网目尺寸和低顺序参数的统一性的最佳性。