Approximation theory for the hp-version finite element method and application to the non-linear Laplacian

Applied Numerical Mathematics

Volumn 34, Issue 4, 2000, Pages 329-344

  Ainsworth, Mark ^a   Kay, David ^b  

^a UNIVERSITY OF STRATHCLYDE   (United Kingdom)

^b UNIVERSITY OF OXFORD   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; COMPUTATIONAL GEOMETRY; ERROR ANALYSIS; FINITE ELEMENT METHOD; PROBLEM SOLVING; SET THEORY;

NONLINEAR LAPLACIAN;

DIFFERENTIAL EQUATIONS;

EID: 0034249424     PISSN: 01689274     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0168-9274(99)00040-9     Document Type: Article

References (13)

1. R.A. Adams, Sobolev Spaces, Academic Press, 1978.
2. M. Ainsworth, D. Kay, The approximation theory for the p-version finite element method and application to non-linear elliptic PDEs, Numer. Math., to appear.
3. I. Babuška, M. Suri, The h-p version of the finite element method with quasiuniform meshes, Math. Modelling Numer. Anal. 21 (1987) 199-238.
4. I. Babuška, M. Suri, The optimal convergence rate of the p version of the finite element method, SIAM J. Numer. Anal. 24 (1987) 750-776.
5. I. Babuska, B.A. Szabo, I.N. Katz, The p version of the finite element method, SIAM J. Numer. Anal. 18 (1981) 512-545.
6. J.W. Barrett, W.B. Liu, Finite element approximation of the p-Laplacian, Math. Comp. 61 (1993) 523-537.
7. J.W. Barrett, W.B. Liu, Quasi-norm error bounds for the finite element approximation of some degenerate quasilinear elliptic equations and variational inequalities, Math. Modelling Numer. Anal. 28 (1994) 725-724.
8. J. Bergh, J. Löfström, Interpolation Spaces: An Introduction, Springer, Berlin, 1976.
9. S.S. Chow, Finite element error estimates for non-linear elliptic equations of the monotone type, Numer. Math. 54 (1989) 373-393.
10. P.G. Ciarlet, The Finite Element Method for Elliptic Problems, North-Holland, Amsterdam, 1980.
11. M. Dobrowolski, On quasilinear elliptic equations in domains with Conical boundary points, J. Reine Angew. Math. 394 (1989) 186-195.
12. T. Dupont, R. Scott, Polynomial approximation of functions in Sobolev spaces, Math. Comp. 34 (1980) 441-463.
13. P. Tolksdorf, Invariance properties and special structures near conical boundary points, in: W. Wendland, P. Grisvard and J.R. Whiteman, Eds., Lecture Notes in Mathematics, Vol. 1121, Springer, Berlin, 1985, pp. 308-318.