A general Uzawa-type method for a class of 2 × 2 block structure linear system. (15th September 2021) - Miao, Shu-Xin
Abstract: Numerical methods for Navier-Stokes equation and elasticity problem lead to a class of 2 × 2 block structure linear system. Based on a general splitting for the (1, 1) block of coefficient matrix and the Uzawa method, we consider a general Uzawa-type method for solving this 2 × 2 block structure linear system in this paper. With different choices of splitting matrix, the proposed Uzawa-type method includes some existing Uzawa-type methods as its special cases. The convergence and semi-convergence of the proposed method for solving nonsingular and singular problems are studied, respectively. When the splitting matrix is used as a preconditioner, we analyze the spectral properties of the preconditioned matrix. Numerical results are presented to verify the efficiency of the proposed method.