Least squares preconditioning for mixed methods with nonconforming trial spaces
Least squares preconditioning for mixed methods with nonconforming trial spaces
复制标题
具有非一致性试验空间的混合方法的最小二乘预处理
作者：
C. Bacuta;Jacob Jacavage
摘要我们考虑一个具有一致性检验空间和一致性检验空间的混合方法的预处理技术。我们的方法是基于混合方法的鞍点离散理论和对称正定算子的预处理理论。提出了求解离散混合公式的有效迭代过程，并提供了离散相容空间的选择。对于离散化，只需要一个基的测试空间和组装的全球鞍点系统是避免的。我们提供的离散化和迭代误差的逼近性质，并提供了一个尖锐的估计所提出的算法的收敛速度的条件数的椭圆预条件和离散和常数对离散空间。我们专注于应用椭圆偏微分方程的不连续系数。二维和三维域的数值结果包括支持所提出的方法。
ABSTRACT We consider a preconditioning technique for mixed methods with a conforming test space and a nonconforming trial space. Our method is based on the classical saddle point disccretization theory for mixed methods and the theory of preconditioning symmetric positive definite operators. Efficient iterative processes for solving the discrete mixed formulations are proposed and choices for discrete compatible spaces are provided. For discretization, a basis is needed only for the test spaces and assembly of a global saddle point system is avoided. We provide approximation properties for the discretization and iteration errors and also provide a sharp estimate for the convergence rate of the proposed algorithm in terms of the condition number of the elliptic preconditioner and the discrete and constants of the pair of discrete spaces. We focus on applications to elliptic PDEs with discontinuous coefficients. Numerical results for two- and three-dimensional domains are included to support the proposed method.