an:01892318
Zbl 1094.76542
Naff, R. L.; Russell, T. F.; Wilson, J. D.
Shape functions for velocity interpolation in general hexahedral cells
EN
Comput. Geosci. 6, No. 3-4, 285-314 (2002).
00089449
2002
j
76M10 76S05
control-volume method; CVMFE method; distorted grid; hexahedral grid; local Darcy law; local mass conservation; mixed method; Piola transformation; vector shape function; 3-D
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.