Optimal l estimates for the finite element method on irregular meshes

Mathematics of Computation

Volumn 30, Issue 136, 1976, Pages 681-697

  Scott, Ridgway ^a  

^a BROOKHAVEN NATIONAL LABORATORY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84966250424     PISSN: 00255718     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0025-5718-1976-0436617-2     Document Type: Article

References (27)

1. I. BABUSKA and A. K. AZIZ, Survey lectures on the mathematical foundations of the finite element method, The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations, Academic Press, New York, 1972, 3-359.
2. J. H. BRAMBLE and S. R. HILBERT, Bounds for a class of linear functionals with applications to Hermite interpolation, Numer. Math., v. 16, 1970, 362-369
3. J. H. BRAMBLE, J. NITSCHE and A. SCHATZ, Maximum norm interior estimates for Ritz Galerkin methods, Math. Comp., v. 29, 1975, 677-688.
4. J. H. BRAMBLE and A. H. SCHATZ, Interior maximum norm and super convergence estimates for spline projections, Rev. Franaise Automat. Informat. Recherche Operationnelle Ser. Rouge. (To appear.)
5. J. H. BRAMBLE and A. H. SCHATZ, Higher order local accuracy by averaging in the finite element method, Mathematical Aspects of Finite Elements in Partial Differential Equations, Academic Press, New York, 1974, 1-14.
6. J. H. BRAMBLE and V. THOMEE, Interior maximum norm estimates for some simple finite element methods, Rev. Franaise Automat. Informat. Recherche Operationnelle Ser. Rouge, v. 8, 1974, 5-18
7. A. P. CALDERON, Lebesgue Spaces of Differentiable Functions and Distributions, Proc. Sympos. Pure Math., vol. 4, Providence, R.I., 1961, 33-49.
8. P. G. CIARLET and P. A. RAVIART, Maximum principle and uniform convergence for the finite element method, Comput. Methods Appl. Mech. Engrg., v. 2, 1973, 17-31.
9. J. DOUGLAS, T. DUPONT and L. WAHLBIN, Optimal error estimates for Galerkin approximations to solutions of two-point boundary value problems, Math. Comp., v. 29, 1975, 475-483.
10. J. DOUGLAS, T. DUPONT and M. F. WHEELER, An L estimate and a super convergence result for a Galerkin method for elliptic equations based on tensor products of piece wise polynomials, Rev. Franaise Automat. Informat. Recherche Operationnelle Ser. Rouge, v. 8, 1974, 61-66
11. T. DUPONT and R. SCOTT, Polynomial approximation of functions in Sobolev spaces. (To appear.)
12. I. FRIED, Finite element method Accuracy at a point, Quart. Appl. Math., v. 32, 1974, 149-161.
13. F. JOHN and L. NIRENBERG, On functions of bounded mean oscillation, Comm. Pure Appl. Math, v. 14, 1961, 415-426
14. F. NATTERER, Uber die punktweise Konvergenz Finiter Elemente, Numer. Math., v. 25, 1975, 67-77.
15. J. A. NITSCHE, Lineare Spline Funktionen und die Methoden von Ritz for elliptische Randwertprobleme, Arch. Rational Mech. Anal., v. 36, 1970, 348-355
16. J. NITSCHE, L Convergence of Finite Element Approximation, 2nd Conf. on Finite Elements, Rennes, France, 1975.
17. J. NITSCHE and A. SCHATZ, Interior estimates for Ritz Galerkin methods, Math. Comp., v. 28, 1974, 937-958.
18. G. O. OKIKIOLU, Aspects of the Theory of Bounded Integral Operators in iP Spaces, Academic Press, London, 1971.
19. J. PEETRE, Espaces dinterpolation et theoreme de Soboleff, Ann. Inst. Fourier Grenoble, v. 16, 1966, pp. 279-317.
20. A. SCHATZ and L. WAHLBIN, Interior maximum norm estimates for finite element methods. (To appear.)
21. R. SCOTT, Finite element convergence for singular data, Numer. Math., v. 21, 1973, 317-327.
22. G. STRANG and G. FIX, A Fourier Analysis of the Finite Element Variational Method. (Unpublished manuscript.)
23. G. STRANG and G. FIX, An Analysis of the Finite Element Method, Prentice-Hall, Englewood Cliffs, N.J., 1973.
24. E. M. STEIN, Singular Integrals and Differentiability Properties of Functions, Princeton Math. Ser., 30, Princeton Univ. Press, Princeton, N.J., 1970
25. E. M. STEIN and G. WEISS, Introduction to Fourier Analysis on Euclidean Spaces, Princeton Math. Ser., 32, Princeton Univ. Press, Princeton, N.J., 1971
26. L. WAHLBIN, On maximum norm error estimates for Galerkin approximations to one dimensional second order parabolic boundary value problems, SIAM J. Numer. Anal., v. 12, 1975, 177-182.
27. M. F. WHEELER, L estimates of optimal orders for Galerkin methods for one-dimensional second order parabolic and hyperbolic equations, SIAM J. Numer. Anal., v. 10, 1973, 908-913.