63 |
In this case, triangles have been used but other forms of subdivisions |
In this case, triangles have been used but other forms of subdivisions |

64 |
can be constructed, e.g. into quadrilaterals or, in the three dimensional case, into tetrahedrons |
can be constructed, e.g. into quadrilaterals or, in the three dimensional case, into tetrahedrons |

65 |
and hexahedrons. The idea of the finite element method is to approximate the solution by a function |
and hexahedrons. The idea of the finite element method is to approximate the solution by a function |

66 |
which is a polynomial of a certain order and is continuous across it boundary to neighbour elements. |
which is a polynomial of a certain order and is continuous across it boundary to neighbor elements. |

67 |
In the example of \fig{FINLEY FIG 0} a linear polynomial is used on each triangle. As one can see, the triangulation |
In the example of \fig{FINLEY FIG 0} a linear polynomial is used on each triangle. As one can see, the triangulation |

68 |
is quite a poor approximation of the ellipse. It can be improved by introducing a midpoint on each element edge then |
is quite a poor approximation of the ellipse. It can be improved by introducing a midpoint on each element edge then |

69 |
positioning those nodes located on an edge expected to describe the boundary, onto the boundary. |
positioning those nodes located on an edge expected to describe the boundary, onto the boundary. |