Jacobians for isoparametric finite elements

Communications in Numerical Methods in Engineering

Volumn 12, Issue 11, 1996, Pages 755-766

  Barrett, K E ^a  

^a Faculty of Engineering and Computing   (United Kingdom)

Author keywords

Finite elements; Isoparametric; Jacobian; Transformation; Valid

Indexed keywords

ALGORITHMS; BOUNDARY ELEMENT METHOD; MATHEMATICAL MODELS; MATHEMATICAL TRANSFORMATIONS;

ISOPARAMETRIC FINITE ELEMENTS; JACOBIAN DETERMINANT;

FINITE ELEMENT METHOD;

EID: 0030285616     PISSN: 10698299     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1099-0887(199611)12:11<755::AID-CNM15>3.0.CO;2-S     Document Type: Article

References (10)

1. A. R. Mitchell, G. Phillips and E. Wachspress, 'Forbidden shapes in the finite element method', J. Inst. Math. Appl., 8, 260-269 (1971).
2. K. E. Barrett, 'Geometry of the six-noded element', Finite Element News, 2, 16-26 (1995).
3. M. L. Baart and E. J. Mulder, 'A note on invertible two-dimensional quadratic finite element transformations', Commun. Appl. Numer. Methods, 3, 535-539 (1987).
4. D. A. Field, 'Algorithms for determining invertible two- and three-dimensional quadratic isoparametric finite element transformations', Int. j. numer. methods eng., 19, 789-802 (1983).
5. A. E. Frey, C. A. Hall and T. A. Porsching, 'Some results on the global inversion of bilinear and quadratic isoparametric finite element transformations', Math. Comput., 32, 725-749 (1978).
6. P. M. Knupp, 'On the invertibility of the isoparametric map', Commun. Methods Appl. Mech., 78, 313-329 (1990).
7. D. A. Field, 'An algorithm for determining invertible quadratic isoparametric finite element transformations', Math. Comput., 37, 347-360 (1981).
8. M. L. Baart and R. J. Y. McLeod, 'Quadratic transformations of triangular finite elements in two dimensions', IMA J. Numer. Anal., 6, 475-487 (1986).
9. K. H. Huebner, The Finite Element Method for Engineers, Wiley, 1975.
10. A. C. Aitken, Determinants and Matrices, Oliver and Boyd, 1956, p. 44.