Fig. 5

Example of a conforming nodal cell centered on node \(L\) and located at \({\mathbf{x}}_{L}\); shape functions for calculating smoothed gradients are evaluated at the center of each nodal boundary segment, \({\mathbf{x}}_{L}^{{\Gamma }_{i}}\), which have outward normals \({\mathbf{n}}_{L}^{{\Gamma }_{i}}\); shape functions for calculating the pressure projection are evaluated at the centroids of the sub-cells, \({\mathbf{x}}_{L}^{{S}_{i}}\); the sub-cell areas are denoted by \({A}_{L}^{{S}_{i}}\)