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Analysis of mixed methods using conforming and nonconforming finite element methods. (English) Zbl 0784.65075
The main purpose of this paper is to derive error estimates of mixed finite element methods for second order elliptic problems with variable coefficients, where the emphasis is on variable coefficients.
At first assuming that the coefficients are piecewise constant, the author proves the equivalence between four mixed methods proposed by P. A. Raviart and J. M. Thomas [Lect. Notes Math. 606, 292-315 (1977; Zbl 0362.65089)], F. Brezzi, J. Douglas jun., and L. D. Marini [Numer. Math. 47, 217-235 (1985; Zbl 0599.65072)] and L. Marini and P. Pietra [Mat. Apl. Comput. 8, No. 3, 219-239 (1989; Zbl 0711.65091)] with modified conventional conforming and nonconforming finite element methods. Afterwards he extends the results to the case of variable coefficients in detail only for the lowest-order Raviart-Thomas method. For the other cases he refers to his own Ph. D. thesis.

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
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References:
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