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.

中文翻译：

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用于具有参数相关低阶项的椭圆算子的HDG方法的均匀辅助空间预处理

辅助空间预处理（ASP）技术应用于具有参数相关的低阶项的三个不同椭圆问题的HDG方案，即，用于标量反应扩散方程的对称内罚HDG方案，用于散度的HDG方案。一个低阶项的广义双调和方程的矢量反应扩散方程和C 0连续内罚HDG格式。对于每种情况，都获得了统一的预处理器，J。Xu [21]的通用ASP理论用于证明网格尺寸的最佳性和低阶参数的均匀性。