## Preconditioning of nonconforming finite element methods for second-order elliptic boundary value problems

This thesis deals with the condition numbers and singular value distribution of the preconditioned operators B[sub h][sup [minus]1]A[sub h] and A[sub h]B[sub h][sup [minus]1], where A[sub h] and B[sub h] are nonconforming finite element discretizations of second-order elliptic operators A and B. It generalizes the works of Manteuffel and Parter, Goldstein, Manteuffel and Parter, as well as Parter and Wong. Three nonconforming finite element methods are considered. The first two methods, the penalty method and the method of nearly-zero boundary conditions, deal with Dirichlet boundary conditions on curved domains. It is shown that if the leading part of A ismore »