## Abstract

Quadrilateral finite elements are generally constructed by starting from a given finite dimensional space of polynomials V̂ on the unit reference square K̂. The elements of V̂ are then transformed by using the bilinear isomorphisms F_{K} which map K̂ to each convex quadrilateral element K. It has been recently proven that a necessary and sufficient condition for approximation of order r + 1 in L^{2} and r in H^{1} is that V̂ contains the space Qr of all polynomial functions of degree r separately in each variable. In this paper several numerical experiments are presented which confirm the theory. The tests are taken from various examples of applications: The Laplace operator, the Stokes problem and an eigenvalue problem arising in fluid-structure interaction modelling.

Original language | English (US) |
---|---|

Pages (from-to) | 805-812 |

Number of pages | 8 |

Journal | Communications in Numerical Methods in Engineering |

Volume | 17 |

Issue number | 11 |

DOIs | |

State | Published - Nov 2001 |

## Keywords

- Approximation
- Fluid-structure interaction
- Laplace operator
- Mixed finite element
- Quadrilateral finite elements
- Serendipity
- Stokes problem