 # Diff of /trunk/doc/user/finley.tex

revision 1459 by ksteube, Thu Mar 27 01:49:10 2008 UTC revision 1700 by lgraham, Thu Aug 14 03:35:46 2008 UTC
# Line 63  subdivision of an ellipse into so called Line 63  subdivision of an ellipse into so called
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.

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