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On mixed finite element methods for first order elliptic systems. (English) Zbl 0459.65072

MSC:
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35F30 Boundary value problems for nonlinear first-order PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
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References:
[1] Babuska, I., Aziz, A.K.: Mathematical foundations of the finite element method. New York: Academic Press 1972
[2] Babuska, I., Oden, J.T., Lee, J.K.: Mixed hybrid finite element approximation of second order elliptic boundary value problems. Comput. Methods Appl. Mech. Engrg.14, 1-23 (1978) · Zbl 0401.65068
[3] Brezzi, F.: On the existence, uniqueness and application of saddle point problems arising from lagrange multipliers. R.A.I.R.O.8, 129-150 (1975)
[4] Ciarlet, P.G.: The finite element method for elliptic problems. Amsterdam: North Holland Publishing 1977
[5] Fix, G.J., Gunzburger, M.D., Nicolaides R.A.: Theory and applications of mixed finite element methods. Constructive approaches to mathematical models. New York: Academic Press, pp. 375-393, 1979 · Zbl 0459.65071
[6] Lions, J.L., Magenes, E.: Nonhomogeneous Boundary Value problems. Springer, 1973 · Zbl 0251.35001
[7] Raviart, P.A., Thomas, J.M.: A mixed finite element method for second-order elliptic problems. Mathematical aspects of finite element methods. Rome 1975: Lecture Notes in Mathematics, Springer
[8] Serrin, J.: Mathematical Principles of Classical Fluid Mechanics, In: Encyclopedia of Physies,8, No. 1, pp. 125-350 (1959) (Section 24)
[9] Strang, G., Fix, G.: An analysis of the finite element method. New York: Prentice-Hall 1973 · Zbl 0356.65096
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