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Zur \(L^\infty\)-Konvergenz linearer finiter Elemente beim Dirichlet- Problem. (German) Zbl 0321.65055

MSC:
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
35J55 Systems of elliptic equations, boundary value problems (MSC2000)
65J05 General theory of numerical analysis in abstract spaces
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References:
[1] Agmon, S.: Lectures on elliptic boundary value problems. Princeton: van Nostrand 1965 · Zbl 0142.37401
[2] Bramble, J. H., Hilbert, S. R.: Bounds on a class of linear functionals with applications to Hermite interpolation. Numerische Math.16, 362-369 (1971) · Zbl 0214.41405 · doi:10.1007/BF02165007
[3] Campanato, S.: Equazioni ellittiche del IIo ordine e spaziL 2, ?). Ann. Mat. pura appl., IV. Ser.69, 321-381 (1965) · Zbl 0145.36603 · doi:10.1007/BF02414377
[4] Frehse, J., Rannacher, R.: EineL 1-Fehlerabschätzung diskreter Grundlösungen in der Methode der finiten Elemente. Tagungsband ?Finite Elemente?, Bonn. Math. Schr. 1976 · Zbl 0359.65093
[5] Natterer, F.: Über die punktweise Konvergenz finiter Elemente. Numer. Math.25, 67-77 (1975) · Zbl 0331.65073 · doi:10.1007/BF01419529
[6] Nitsche, J.: Lineare Spline Funktionen und die Methode von Ritz für elliptische Randwertaufgaben. Arch. rat. Mech. Analysis36, 348-355 (1970) · Zbl 0192.44503 · doi:10.1007/BF00282271
[7] Nitsche, J.:L ?-convergence of finite element approximation. Preprint, 2. Converence on Finite Elements, Rennes, France 1975
[8] Piccinini, L. C.: Proprietà di inclusione e interpolazione tra spazi di Morrey e loro generalizzazioni. Tesi di perfezionamento 1969. Scuola Normale Superior Pisa
[9] Scott, R.: OptimalL ?-estimates for the finite element method on irregular meshes. Preprint
[10] Zlamal, M.: Curved elements in the finite element method. I. SIAM J. numer. Analysis10, 229-240 (1973), II. SIAM J. Numer. Analysis11, 347-362 (1974) · Zbl 0285.65067 · doi:10.1137/0710022
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