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$L^\infty$-convergence of finite element approximation to quasilinear initial boundary value problems. (English) Zbl 0408.65067

65N30Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (BVP of PDE)
65N12Stability and convergence of numerical methods (BVP of PDE)
65N15Error bounds (BVP of PDE)
35K60Nonlinear initial value problems for linear parabolic equations
Full Text: EuDML
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[3] 3 P. G. CIARLET and P A. RAVIART, General Lagrange and Hermite interpolation in $R^n$ with applications to finite element methods, Arch Rat.Mech Anal., Vol.46, 1972, pp 177-199 Zbl0243.41004 MR336957 · Zbl 0243.41004 · doi:10.1007/BF00252458
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[7] 7. J FREHSE, Optimale gleichmässige Konvergenz der Methode der finiten Elemente bei quasilinearen $N$-dimensionalen Randwertproblemen, Zeitschrift Angew. Math u. Mech., Tagungsband G.A M.M., 1976 (to appear). Zbl0357.65085 MR436622 · Zbl 0357.65085 · doi:10.1002/zamm.19770570405
[8] 8. J. FREHSE and R. RANNACHER, Asymptotic $L^\infty$-error estimates for linear finite element approximations of quasilinear boundary value problems, S.I.A.M J Numer. Anal, (to appear). Zbl0386.65049 MR502037 · Zbl 0386.65049 · doi:10.1137/0715026
[9] 9 J. FREHSE and R RANNACHER, Optimal Uniform Convergence for the Finite Element Approximation of a Quasilinear Elliptic Boundary Value Problem, Preprint. · Zbl 0386.65049
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[17] 17 M. ZLÁMAL, Curved Elements in the Finite Element Methods, I S.I.A M., J Numer Anal., Vol. 10, 1973. pp. 229-249; II. S.I A.M, J. Numer Anal., Vol. 11, 1974, pp. 347-362 MR343660