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On some techniques for approximating boundary conditions in the finite element method. (English) Zbl 0856.65130
The foundations for the theory of mixed finite element methods were laid down by I. Babuška [Numer. Math. 20, 179-192 (1973; Zbl 0258.65108)] who introduced the idea of approximating essential boundary conditions in the Dirichlet problem by using a Lagrange multiplier.
The author recalls the method of Babuška and proposes a simplification of the stabilized formulation of H. J. C. Barbosa and T. J. R. Hughes [Comput. Methods Appl. Mech. Eng. 85, No. 1, 109-128 (1991; Zbl 0764.73077) and Numer. Math. 62, No. 1, 1-15 (1992; Zbl 0765.65102)]. Next he shows that this method is closely related to a classical method by J. Nitsche [Abh. Math. Sem. Univ. Hamburg 36, 9-15 (1971; Zbl 0229.65079)].

MSC:
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
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