Penalized weak form

By calculating the directional derivative with w = rnt v, the penalized weak form [PWF] is obtained as follows ... 

When the viscosity r] is distributed inhomogeneously, an analytical solution of the microscale equations (8.20) and (8.21) is not possible we therefore perform a finite element calculation. We first give a penalized weak form of (8.20) with the... 

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