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

Suri, Manil

Math. Comput. 54, No. 189, 1-19 (1990).

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

MSC:

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

Keywords:

mixed finite element methods; p-version; h-p-version; convergence; stability