 -\frac{0}{0} \tau _m \int _\varOmega \nabla _{\phi ^m}\cdot {\varvec{v}}^{m}(u^m_h)^0 \, \rho ^m\, |\nabla \phi ^{m}|+ \frac{0}{0} \int _\varOmega (u^m_h)^0 \, \rho ^m\, \bigl ( | \nabla \phi ^{m-0}|