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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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