Efficient rectangular mixed finite elements in two and three space variables

Abstract

Summary: Two families of mixed finite elements for second order elliptic equations are introduced, one in two variables and the other in three. These rectangular elements are related to ones in two space and in three space studied earlier by the authors. They give the same rates of convergence as the corresponding Raviart-Thomas elements with fewer parameters per rectangle. Hybridization of the mixed method for these elements is considered, and alternating-direction iterative techniques are discussed.