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Some asymptotic error estimates for finite element approximation of minimal surfaces. (English) Zbl 0356.35034

MSC:
35J60 Nonlinear elliptic equations
35A35 Theoretical approximation in context of PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N99 Numerical methods for partial differential equations, boundary value problems
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References:
[1] 1. J. H. BRAMBLE, S. R. HILBERT, Bounds on a class of linear functionals with applications to Hermite interpolation, Numer. Math., Vol. 16, 1971, pp. 362-369. Zbl0214.41405 MR290524 · Zbl 0214.41405 · doi:10.1007/BF02165007 · eudml:132041
[2] 2. J. FREHSEEine a-priori-Abschätzung zur Methode der finiten Elemente in der numerischen Variationsrechnung.In : Numerische Behandlung von Variations-und Steuerungsproblem, Tagungsband, Bonn. Math. Schr., Vol. 77, 1975, pp. 115-126. Zbl0316.65027 MR405884 · Zbl 0316.65027
[3] 3. J. FREHSE, Eine gleichmaige asymptotische Fehlerabschätzung zur Methode der finiten Elemente bei quasilinearen Randwertproblemen. In : Theory of Nonlinear Operators. Constructive Aspects, Tagungsband der Akademie der Wissenschaften, Berlin (DDR), 1976. Zbl0368.65054 · Zbl 0368.65054
[4] 4 J FREHSE, R RANNACHER, Eine L1-Fehlerabschatzung fur diskrete Grundlosungen in der Methode der finiten Elemente In Finite Elemente, Tagungsband, Bonn Math Schr, Vol 89, 1976, pp 92-114 Zbl0359.65093 · Zbl 0359.65093
[5] 5 C JOHNSON, V THOMEE, Error estimates for a finite element approximation of a minimal surface, Math Comp , Vol 29, 1975, pp 343-349 Zbl0302.65086 MR400741 · Zbl 0302.65086 · doi:10.2307/2005555
[6] 6 H D MITTELMANN, On pointwise estimates for a finite element solution of nonlinear boundary value problems To appear Zbl0367.65059 MR445865 · Zbl 0367.65059 · doi:10.1137/0714053
[7] 7 C B MORREY, Multiple intégrals in the calculus of variations Springer Berlm-Heidelberg-New York, 1966 Zbl0142.38701 MR202511 · Zbl 0142.38701
[8] 8 F NATTERER, Uber die punktweise Konvergenz finiter Elemente Numer Math,Vol 25 1975 pp 67-77 Zbl0331.65073 MR474884 · Zbl 0331.65073 · doi:10.1007/BF01419529 · eudml:132361
[9] 9 J NECAS, Les méthodes directes en théorie des équations elliptiques Masson, Paris, 1967 Zbl1225.35003 · Zbl 1225.35003
[10] 10 J NITSCHE, Lineare Spline-Funktionen und die Methode von Ritz fur elliptische Randweirtaufgaben Arch Rational Mech Anal, Vol 36, 1970, pp 348-355 Zbl0192.44503 MR255043 · Zbl 0192.44503 · doi:10.1007/BF00282271
[11] 11 J NITSCHE, L \infty -convergence of finite element approximation 2 Conference on Finite Eléments, Rennes (France), 1975 MR568857
[12] 12 R RANNACHER, Zur L \infty -Konvergenz linearer finiter Elemente Math Z, Vol 149, 1976 pp 69-77 Zbl0321.65055 MR488859 · Zbl 0321.65055 · doi:10.1007/BF01301633 · eudml:172382
[13] 13 R SCOTT, Optimal Lx-estimates Jot the finite element method on irregular meshes Math Comp, Vol 30, 1976 Zbl0349.65060 MR436617 · Zbl 0349.65060 · doi:10.2307/2005390
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