On the stability and convergence of higher-order mixed finite element methods for second-order elliptic problems. (English) Zbl 0687.65101

The author investigates the use of some mixed methods for which convergence depends upon two factors - the stability of the subspaces used and their approximation properties. The author determines how the stability constants for these spaces behave when p is increased. This is necessary to find whether when the p- and the h-p version whould be stable if these methods are used. The rates of convergence for these methods which are uniform in both h and p are given. For analysis the elements of P. A. Raviart and J. M. Thomas [Lect. Notes Math. 606, 292-315 (1977; Zbl 0362.65089)] and of F. Brezzi, J. Douglas jun., and L. D. Marini [Numer. Math. 47, 217-235 (1985; Zbl 0599.65072)] are tested.
Reviewer: P.Chocholatý


65N30 Finite element, Rayleigh-Ritz and Galerkin 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
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