A new family of mixed finite element spaces over rectangles. (English) Zbl 0806.65109

Douglas, Jim jun.; Wang, Junping

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)

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