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\(L_\infty\)-convergence of saddle-point approximations for second order problems. (English) Zbl 0356.35026

MSC:
35J25 Boundary value problems for second-order elliptic equations
35J35 Variational methods for higher-order elliptic equations
35A35 Theoretical approximation in context of PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
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References:
[1] 1. P. G. CIARLET and P.A. RAVIARTG, General Lagrange and Hermite interpolation in Rn with applications to finite element methods. Archive Rational Mech. Anal., Vol. 46, 1972, pp. 177-199. Zbl0243.41004 MR336957 · Zbl 0243.41004 · doi:10.1007/BF00252458
[2] 2. F. NATTERER, Über die punkweise Konvergenz finiter Elemente, Numer. Math., Vol.25, 1975. pp. 67-77, Zbl0331.65073 MR474884 · Zbl 0331.65073 · doi:10.1007/BF01419529 · eudml:132361
[3] 3. J. NITSCHE, \(L_\infty\)- convergence of finite element approximation, Second Conference on Finite Elements, Rennes, France. (To appear). MR568857
[4] 4. J. NITSCHE, Über \(L_\infty\)-Abschätzungen von Projektionen auf finite Elemente, Bonner Mathematische Schriften Vol. 89, 1976, pp. 13-30. Zbl0358.65094 MR451780 · Zbl 0358.65094
[5] 5. P. A. RAVIART and J. M. THOMAS, A mixed finite element method for second order elliptic problems. (To appear). Zbl0362.65089 · Zbl 0362.65089
[6] 6. R. SCHOLZ, Approximation von Sattelpunkten mit finiten Elementen, Bonner Mathe-matische Schriften Vol. 89, 1976, pp, 53-66. Zbl0359.65096 MR471377 · Zbl 0359.65096
[7] 7. YOSIDA, Functional analysis, Springer Verlag, Berlin-Heidelberg-New York, 1965. Zbl0126.11504 · Zbl 0126.11504
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