## Mixed finite element methods over quadrilaterals.(English)Zbl 0813.65120

Dimov, I. T. (ed.) et al., Proceedings of the third international conference on advances in numerical methods and applications $$O(h^ 3)$$, Sofia, Bulgaria, 21-26 August, 1994. Singapore: World Scientific. 203-214 (1994).
A second-order 2D elliptic equation with Dirichlet boundary condition is considered. The mixed finite element method provides a direct approximation of the flux variable. The rectangular mixed finite elements of P. A. Raviart and J. M. Thomas [Lect. Notes Math. 606, 292-315 (1977; Zbl 0362.65089)], F. Brezzi, J. Douglas jun., M. Fortin and L. D. Marini [Mathematical Modelling and Numerical Analysis 21, No. 4, 581-604 (1987; Zbl 0689.65065)], and J. Douglas jun. and J. Wang [Comput. Appl. Math., 12, No. 3, 183- 197 (1993; Zbl 0806.65109)] are extended to arbitrary convex quadrilaterals. Some quadrilateral elements are presented and their stability is established. Error estimates for quadrilateral approximations are obtained.
For the entire collection see [Zbl 0801.00040].
Reviewer: V.Arnautu (Iaşi)

### MSC:

 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs 65N15 Error bounds for boundary value problems involving PDEs 35J25 Boundary value problems for second-order elliptic equations

### Citations:

Zbl 0362.65089; Zbl 0689.65065; Zbl 0806.65109