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Recent results on mixed finite element methods for second order elliptic problems. (English) Zbl 0611.65071

Vistas in applied mathematics. Numerical analysis, atmospheric sciences, immunology, dedic. G. I. Marchuk occas. 60th birthday, 25-43 (1986).
[For the entire collection see Zbl 0589.00015.]
The paper summarizes the basic features of the mixed Brezzi-Douglas- Marini (BDM) finite element methods. More recent results can be found in the papers by the first two authors, R. Duran and M. Fortin [Mixed finite elements for second order elliptic problems in three variables, Numer. Math. 51, 237-250 (1987)] and by the authors and M. Fortin [RAIRO, Modelisation Math. Anal. Numer. (to appear)]. The application of the BDM elements to linear elasticity problems (Sect. 5) is new and has not been published elsewhere.

MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
74S05 Finite element methods applied to problems in solid mechanics
74B05 Classical linear elasticity
35J15 Second-order elliptic equations

Citations:

Zbl 0589.00015