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On Higher Order Pyramidal Finite Elements

  • Liping Liu (a1), Kevin B. Davies (a1), Michal Křížek (a2) and Li Guan (a3)

Abstract

In this paper we first prove a theorem on the nonexistence of pyramidal polynomial basis functions. Then we present a new symmetric composite pyramidal finite element which yields a better convergence than the nonsymmetric one. It has fourteen degrees of freedom and its basis functions are incomplete piecewise triquadratic polynomials. The space of ansatz functions contains all quadratic functions on each of four subtetrahedra that form a given pyramidal element.

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Corresponding author

Corresponding author. URL: http://www.math.cas.cz/~krizek Email: liping.liu@lakeheadu.ca

References

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[1] Cools, R., Monomial cubature rules since “Stroud”: a compilation-part II, J. Comput. Appl. Math., 112 (1999), pp. 2127.
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[3] Keast, P., Moderate degree tetrahedral quadrature formulas, Comput. Methods. Appl. Mech. Engrg., 55 (1986), pp. 339348.
[4] Křížek, M., and Neittaanmäki, P., Finite Element Approximation of Variational Problems and Applications, Pitman Monographs and Surveys in Pure and Applied Mathematics, Vol. 50, Longman Scientific & Technical, Harlow, 1990.
[5] Liu, L., Davies, K. B., Yuan, K., and Křížek, M., On symmetric pyramidal finite elements, Dynam. Cont. Dis. Ser. B., 11 (2004), pp. 213227.
[6] Wieners, C., Conforming discretizations on tetrahedrons, pyramids, prisms and hexahedrons, Univ. Stuttgart, Bericht 97/15, 1997, pp. 19.
[7] Zlámal, M., The finite element method in domains with curved boundaries, Int. J. Numer. Methods. Engrg., 5 (1972/73), pp. 367373.

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