hp-approximation theory for BDFM and RT finite elements on quadrilaterals

SIAM Journal on Numerical Analysis

Volumn 40, Issue 6, 2002, Pages 2047-2068

  Ainsworth, Mark ^a   Pinchedez, Katia ^a  

^a UNIVERSITY OF STRATHCLYDE   (United Kingdom)

Author keywords

Corner singularities; Exponential convergence; Mixed hp finite elements

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; ELASTICITY; FINITE ELEMENT METHOD; FUNCTIONS; HARMONIC ANALYSIS; INTEGER PROGRAMMING; MAXWELL EQUATIONS; POLYNOMIALS; POROUS MATERIALS; PROBLEM SOLVING; VARIATIONAL TECHNIQUES;

CORNER SIGULARITIES; EXPONENTIAL CONVERGENCE;

APPROXIMATION THEORY;

EID: 0141962816     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036142901391128     Document Type: Article

References (23)

1. M. AINSWORTH AND B. SENIOR, Aspects of an adaptive hp-finite element method: Adaptive strategy, conforming approximation and efficient solvers, Comput. Methods Appl. Mech. Engrg., 150 (1997), pp. 65-87.
2. I. BABUŠKA AND B. Q. Guo, Regularity of the solution of elliptic problems with piecewise analytic data. Part I. Boundary value problems for linear elliptic equation of second order, SIAM J. Math. Anal., 19 (1988), pp. 172-203.
3. I. BABUŠKA AND B. Q. Guo, Regularity of the solution of elliptic problems with piecewise analytic data, II: The trace spaces and application to the boundary value problems with nonhomogeneous boundary conditions, SIAM J. Math. Anal., 20 (1989), pp. 763-781.
4. I. BABUŠKA, B. Guo, AND E. STEPHAN, On the exponential convergence of the hp-version for boundary element Galerkin methods on polygons, Math. Methods Appl. Sci., 12 (1990), pp. 413-427.
5. I. BABUŠKA, R. KELLOGG, AND J. PITKÄRANTA, Direct and inverse error estimates for finite elements with mesh refinements, Numer. Math., 33 (1979), pp. 447-471.
6. I. BABUŠKA AND M. SURI, On locking and robustness in the finite element method, SIAM J. Numer. Anal., 29 (1992), pp. 1261-1293.
7. I. BABUŠKA AND M. SURI, The p and h-p versions of the finite element method, basic principles and properties, SIAM Rev., 36 (1994), pp. 578-632.
8. A. BOSSAVIT, Computational Electromagnetism. Variational Formulation, Complementarity, Edge Elements, Academic Press, Orlando, FL, 1998.
9. F. BREZZI AND M. FORTIN, Mixed and Hybrid Finite Elements Methods, Springer-Verlag, New York, 1991.
10. P. CIARLET, The Finite Element Method for Elliptic Problems, North-Holland, Amsterdam, 1978.
11. P. GRISVARD, Singularities in Boundary Value Problems, Springer-Verlag, Berlin, Masson, Paris, 1992.
12. B. GUO AND I. BABUŠKA, The hp version of the finite element method. Part I: The basic approximation method, Comput. Mech., 1 (1986), pp. 21-41.
13. B. GUO AND I. BABUŠKA, The hp version of the finite element method. Part II: General results and applications, Comput. Mech., 1 (1986), pp. 203-220.
14. R. HIPTMAIR, Canonical construction of finite elements, Math. Comp., 68 (1999), pp. 1325-1346.
15. R. HIPTMAIR, Higher order Whitney forms, Progress in Electromagnetics Research, 32 (2001), pp. 271-299.
16. R. HIPTMAIR, Higher order Whitney forms-abstract, J. Electromaget. Wave Applic., 15 (2001), pp. 341-342.
17. M. LEE AND F. MILNER, Mixed finite element methods for nonlinear elliptic problems: The hp version, J. Comput. Appl. Math., 85 (1998), pp. 239-261.
18. F. MILNER AND M. SURI, Mixed finite element methods for quasilinear second order elliptic problems: The p-version, RAIRO Modél. Math. Anal. Numér., 26 (1992), pp. 913-931.
19. P. MONK, On the p and hp extension of Nédélec's curl conforming elements, J. Comput. Appl. Math., 53 (1994), pp. 117-137.
20. C. SCHWAB, p- and hp-Finite Element Methods, Theory and Applications in Solid and Fluid Mechanics, Oxford University Press, New York, 1998.
21. R. STENBERG AND M. SURI, An hp error analysis of MITC plate elements, SIAM J. Numer. Anal., 34 (1997), pp. 544-568.
22. M. SURI, On the stability and convergence of higher order mixed finite element methods of second order elliptic problems, Math. Comp., 54 (1990), pp. 1-19.
23. L. VARDAPETYAN AND L. DEMKOWICZ, hp adaptive finite elements in electromagnetics, Comput. Methods Appl. Mech. Engrg., 169 (1999), pp. 331-344.