Scholz, R. Optimal \(L_{\infty}\)-estimates for a mixed finite element method for second order elliptic and parabolic problems. (English) Zbl 0571.65092 Calcolo 20, 355-377 (1983). A mixed finite element method for second order problems is considered. Optimal \(L_{\infty}\)-error estimates for the elliptic as well as for the corresponding parabolic problem are derived. Cited in 11 Documents MSC: 65N15 Error bounds for boundary value problems involving PDEs 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 35J25 Boundary value problems for second-order elliptic equations 35K20 Initial-boundary value problems for second-order parabolic equations Keywords:finite element; second order; Optimal \(L_{\infty }\)-error estimates PDF BibTeX XML Cite \textit{R. Scholz}, Calcolo 20, 355--377 (1983; Zbl 0571.65092) Full Text: DOI OpenURL References: [1] P. Ciarlet,The Finite Element Method for Elliptic Problems, (1978) North-Holland Publ. Comp., Amsterdam-New York-Oxford. · Zbl 0383.65058 [2] J. Douglas Jr.–T. Dupont–L. Wahlbin,The stability in L q of the ion into L 2-projection into finite element function spaces. Numer. Math.23 (1975) 193–197. · Zbl 0297.41022 [3] V. Girault–P. A. Raviart,Finite Element Approximation of the Navier-Stokes Equations, (1979), Springer-Verlag, Berlin-Heidelberg-New York. · Zbl 0413.65081 [4] C. Johnson–V. Thomée,Error estimates for some mixed finite element methods for parabolic type problems, R.A.I.R.O. Anal. Numer.15 (1981), 41–78. · Zbl 0476.65074 [5] F. Natterer,Über die punktweise Konvergenz finiter Elemente, Numer. Math.25 (1975), 67–77. · Zbl 0331.65073 [6] J. Nitsche,L convergence of finite element approximation, 2. Conference on Finite Elements, Rennes, 1975. [7] J. Nitsche,Über L Abschätzungen von Projektionen auf finite Elemente, Bonn. Math. Schr.89 (1976), 13–30. [8] J. Nitsche–M. Wheeler,L boundedness of the finite element Galerkin operator for parabolic problems, (To appear). · Zbl 0533.65071 [9] P.-A. Raviart–J. M. Thomas,A mixed finite element method for 2nd order elliptic problems, Proc. of the Symp. on the Math. Aspects of the Finite Element Method, Rome, (1975), 292–315, (1977), Springer-Verlag, Berlin-Heidelberg-New York. [10] M. Schechter,On L p -estimates and regularity, I. Amer. J. Math.85 (1963), 1–13. · Zbl 0113.30603 [11] R. Scholz,L convergence of saddle-point approximations for second order problems, R.A.I.R.O. Anal. Numér.11 (1977), 209–216. · Zbl 0356.35026 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.