A WEIGHTED H(div) LEAST-SQUARES METHOD FOR SECOND-ORDER ELLIPTIC PROBLEMS.

This paper presents analysis of a weighted-norm least squares finite element method for elliptic problems with boundary singularities. We use H(div) conforming Raviart-Thomas elements and continuous piecewise polynomial elements. With only a rough estimate of the power of the singularity, we employ a simple, locally weighted L² norm to eliminate the pollution effect and recover better rates of convergence. Theoretical results are carried out in weighted Sobolev spaces and include ellipticity bounds of the homogeneous least-squares functional, new weighted Raviart-Thomas interpolation results, and error estimates in both weighted and nonweighted norms. Numerical tests are given to confirm the theoretical estimates and to illustrate the practicality of the method. [ABSTRACT FROM AUTHOR]