- |\nabla \phi ^{m}|+\tau _m (\nabla \phi ^m_t,\nu ^m) \bigr ) + \tau _m \int _\varOmega f^{e,m} u^m_h\, \rho ^m\,|\nabla \phi ^{m}|. \end{aligned}$$\end{document}$$We deduce from ([00](#Equ00){ref-type=""}), Lemma [0](#FPar00){ref-type="sec"}, 