Least-Squares Mixed Finite Element Methods for Non-Selfadjoint Elliptic Problems: II. Performance of Block-ILU Factorization Methods

The least-squares mixed finite element technique developed in Part I is applied to non-selfadjoint second-order elliptic problems. This approach leads to a symmetric positive definite bilinear form which is coercive uniformly in the discretization parameter. In this paper we consider an approximate block-factorization technique recently proposed by Chan and Vassilevski in [A framework for block-ILU factorization using block size reduction, Math. Comp., 64 (1995), pp. 129–156] and which is well defined for positive definite block-tridiagonal matrices. The method is analyzed and supported with extensive numerical experiments.