The partition of unity finite element method: Basic theory and applications

Computer Methods in Applied Mechanics and Engineering

Volumn 139, Issue 1-4, 1996, Pages 289-314

  Melenk, J M ^a   Babuska I ^b  

^a ETH ZURICH   (Switzerland)

^b UNIVERSITY OF TEXAS AT AUSTIN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL METHODS; DIFFERENTIAL EQUATIONS; MATHEMATICAL MODELS; NUMERICAL METHODS; PROBLEM SOLVING;

ONE DIMENSIONAL; PARTITION OF UNITY;

FINITE ELEMENT METHOD;

EID: 0030380578     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0045-7825(96)01087-0     Document Type: Article

References (20)

1. A.K. Aziz and I.M. Babuška, eds., Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations (Academic Press, New York, 1972).
2. I. Babuška and J.E. Osborn, Private communication.
3. S. Bergman, Integral Operators in the Theory of Linear Partial Differential Equations (Springer Verlag, 1961).
4. R.W. Freund, A transpose-free quasi-minimal residual algorithm for non-hermitian linear systems, SIAM J. Sci. Comput. 14(2) (1993) 470-482.
5. I.S. Gradshtein, Table of Integrals, Series and Products (Academic Press, New York, 1980).
6. I. Herrera, Boundary Methods: An Algebraic Theory (Pitman, Boston, 1984).
7. R. Kress, Linear Integral Equations (Springer Verlag, 1989).
8. J.M. Melenk, On generalized finite element methods, Ph.D. Thesis, University of Maryland, 1995.
9. S.N. Mergelyan, Uniform Approximation to Functions of a Complex Variable, Vol. 3 of 1 (AMS, 1962) 294-391.
10. N.I. Muskhelishvili, Some Basic Problems of the Mathematical Theory of Elasticity (P. Noordhoff, Groningen, 1963).
11. Hae-Soo Oh and I. Babuška, The p-version of the finite element method for the elliptic boundary value problems with interfaces, Comput. Methods Appl. Mech. Engrg. 97 (1992) 211-231.
12. Hae-Soo Oh and I. Babuška, The method of auxiliary mapping for the finite element solutions of elasticity problems containing singularities, J. Comput. Phys. 121(2) (1995) 193-212.
13. I. Babuška, G. Caloz and J. Osborn, Special finite element methods for a class of second order elliptic problems with rough coefficients, SIAM J. Numer. Anal. 31 (1994) 945-981.
14. I. Babuška, F. Ihlenburg, E. Paik and S. Sauter, A generalized finite element method for solving the Helmholtz equation in two dimensions with minimal pollution, Comput. Methods Appl. Mech. Engrg. 128 (1995) 325-360.
15. I. Babuška and J.M. Melenk, The partition of unity method, Int. J. Numer. Methods Engrg., in press.
16. I. Babuška and Z. Zhang, The partition of unity finite element method for the elastically supported beam, to appear.
17. G. Szegö, Über Polynome, die zu einer gegebenen Kurve der komplexen Ebene gehören. Mathematische Zeitschrift 9 (1921) 218-270.
18. L.L. Thomson and P.M. Pinsky, A Galerkin least squares finite element method for the two-dimensional Helmholtz equation, Int. J. Numer. Methods Engrg. 38 (1995) 371-397.
19. I.N. Vekua, New Methods for Solving Elliptic Equations (North Holland, 1967).
20. J.L. Walsh, Interpolation and Approximation by Rational Functions in the Complex Domain, Vol. 20 of Colloquium Publications (AMS, 1960).