Douglas, Jim jun.; Wang, Junping A new family of mixed finite element spaces over rectangles. (English) Zbl 0806.65109 Comput. Appl. Math. 12, No. 3, 183-197 (1993). The article is concerned with fixed finite element methods for second- order elliptic boundary value problems. A new family of finite element spaces with rectangular elements is introduced which provide, in comparison with other elements, a simpler structure of the resulting linear algebraic equations, while the convergence rate for the flux variable stays the same. Besides corresponding results on error estimates and on super-convergence at selected points, the authors present some iterative solution methods for the resulting system, including the alternating directions method and a modified Schwarz alternating method. Finally, the new finite element spaces are generalized to the three- dimensional case. Reviewer: M.Plum (Clausthal-Zellerfeld) Cited in 1 ReviewCited in 6 Documents MSC: 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs 65N15 Error bounds for boundary value problems involving PDEs 65F10 Iterative numerical methods for linear systems 35J25 Boundary value problems for second-order elliptic equations Keywords:alternating directions method; finite element methods; second-order elliptic boundary value problems; convergence; error estimates; super- convergence; iterative solution methods; Schwarz alternating method PDF BibTeX XML Cite \textit{J. Douglas jun.} and \textit{J. Wang}, Comput. Appl. Math. 12, No. 3, 183--197 (1993; Zbl 0806.65109)