I have a problem with this finite element formulation.After applied a Splitting Operator $Q=\hat{Q} + \tilde{Q}$ I do not know how to procede.I need to obtain the solution of the following finite element formulation: given $A_h^{n+1}$ and $\hat{Q}_h^{n+1}$, find $\tilde{Q}_h^{n} \in V_h^0$ such that:$\Bigg( \dfrac{1}{A_h^{n+1}}\tilde{Q}_h^{n+1},\phi_h \Bigg) + \dfrac{m}{\rho} \Bigg( \dfrac{\tilde{Q}_h^{n+1}}{\partial z} , \dfrac{\partial \phi_h}{\partial z} \Bigg) = \dfrac{m}{\rho} \Bigg( \dfrac{\hat{Q}_h^{n+1}}{\partial z} , \dfrac{\partial \phi_h}{\partial z} \Bigg), \qquad \forall \phi_h \in V_h^0$ I do not know how to deal in this situation because I have two unknown terms.Thanks.
Splitting Operator
finite element;operator splitting