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``Recent progress on wilson nonconforming finite element''
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Wilson nonconforming finite element (1973) is a very useful recutangular
element in practice. It is shown in many engeneering applications that the
convergence behavier of this element is better than that of the commonly
used bilinear element. However, mathematical studies carried out so far
cannot justify it. I have spent many years on this probolem. The results
obtained by use of standard finite element analysis are not satisfactory.
Recently (2007--) we tackle this problem from a different view point,
i.e. from Mechanics, where the Wilson element was originated. We have
succeeded in proving both mathematically and numerically that the Wilson
element is free of shear locking for a wide class of bending dominated plane
elasticity problems, while the bilinear element suffers from shear locking.
Therefore, we elucidate a long-standing folklore: why Wilson element does
a better job in many practical applications than the bilinear element.