Fig. 3
\(Q_{1}RT_{0}\) Raviart–Thomas finite element and its mapping from the
parametric to the physical space. a The
deformation map \({\varvec{\varphi }}\) is continuously interpolated using node-based
\(\hbox {Q}_{1}\) shape functions. The solvent-volume flux
is approximated using edge-based \(\hbox {RT}_{0}\) shape functions. b To
obtain the \(\hbox {RT}_{0}\) shape functions and their derivatives in the physical
space, a Piola transformation from the parametric space according to
(21) is
considered