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

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