UNIFORM AUXILIARY SPACE PRECONDITIONING FOR HDG METHODS FOR ELLIPTIC OPERATORS WITH A PARAMETER DEPENDENT LOW ORDER TERM
UNIFORM AUXILIARY SPACE PRECONDITIONING FOR HDG METHODS FOR ELLIPTIC OPERATORS WITH A PARAMETER DEPENDENT LOW ORDER TERM
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DOI：
10.1137/20m1382325
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发表时间：
2021-01-01
影响因子：
3.1
通讯作者：
Fu, Guosheng
中科院分区：
文献类型：
--
作者：
Fu, Guosheng
将辅助空间预处理（ASP）技术应用于三种不同的具有参数依赖低阶项的椭圆型问题的可杂交间断Galerkin（HDG）格式，即标量反应扩散方程的对称内罚HDG格式，向量反应扩散方程的一致发散HDG格式，和含低阶项的广义双调和方程的C 0连续内罚HDG格式。对于每种情况和J. Xu的一般ASP理论[Computing，56（1996），pp. 215- 235]用于证明网格尺寸的最优性和低阶参数的均匀性。
The auxiliary space preconditioning (ASP) technique is applied to the hybridizable discontinuous Galerkin (HDG) schemes for three different elliptic problems with a parameter dependent low order term, namely, a symmetric interior penalty HDG scheme for the scalar reactiondiffusion equation, a divergence-conforming HDG scheme for a vectorial reaction-diffusion equation, and a C0-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 [Computing, 56 (1996), pp. 215--235] is used to prove the optimality with respect to the mesh size and uniformity with respect to the low order parameter.