Naff, R. L.; Russell, T. F.; Wilson, J. D. Shape functions for velocity interpolation in general hexahedral cells. (English) Zbl 1094.76542 Comput. Geosci. 6, No. 3-4, 285-314 (2002). Summary: Numerical methods for grids with irregular cells require discrete shape functions to approximate the distribution of quantities across cells. For control-volume mixed finite-element (CVMFE) methods, vector shape functions approximate velocities and vector test functions enforce a discrete form of Darcy’s law. In this paper, a new vector shape function is developed for use with irregular, hexahedral cells (trilinear images of cubes). It interpolates velocities and fluxes quadratically, because as shown here, the usual Piola-transformed shape functions, which interpolate linearly, cannot match uniform flow on general hexahedral cells. Truncation-error estimates for the shape function are demonstrated. CVMFE simulations of uniform and non-uniform flow with irregular meshes show first- and second-order convergence of fluxes in the \(L^2\) norm in the presence and absence of singularities, respectively. Cited in 15 Documents MSC: 76M10 Finite element methods applied to problems in fluid mechanics 76S05 Flows in porous media; filtration; seepage Keywords:control-volume method; CVMFE method; distorted grid; hexahedral grid; local Darcy law; local mass conservation; mixed method; Piola transformation; vector shape function; 3-D PDFBibTeX XMLCite \textit{R. L. Naff} et al., Comput. Geosci. 6, No. 3--4, 285--314 (2002; Zbl 1094.76542) Full Text: DOI