Uniform convergence and two-level Schwarz method for Carey non-conforming element method for non-self-adjoint and indefinite problems.

In this paper, the existence, uniqueness and uniform convergence of the solution of the Carey non-conforming element with non-quasi-uniform partitions is proved for non-self-adjoint and indefinite second-order elliptic problems under a minimal regularity assumption. Furthermore, the optimal error estimate for the solution of Carey non-conforming element method is obtained only under an H2 smoothness hypothesis. Finally, a two-level Schwarz method which suits non-quasi-uniform partitions is proposed and optimal convergence for the pre-conditioned GMRES method is shown. Copyright © 2000 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]