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We present families of scalar nonconforming finite elements of arbitrary
order with optimal approximation properties on quadrilaterals and
hexahedra. Their vector-valued versions together with a discontinuous
pressure approximation of order form inf-sup stable finite element pairs
of order for the Stokes problem. The well-known elements by Rannacher
and Turek are recovered in the case . A numerical comparison between
conforming and nonconforming discretisations will be given. Since higher
order...
The discretisation of the Oseen problem by finite element methods may suffer
in general from two shortcomings. First, the discrete inf-sup
(Babuška-Brezzi)
condition can be violated. Second, spurious oscillations
occur due to the dominating convection. One way to overcome both
difficulties is the use of local projection techniques. Studying
the local projection method in an abstract setting, we show that
the fulfilment of a local inf-sup condition between approximation and
projection spaces...
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