Accuracy of mixed and control volume finite element approximations to Darcy velocity and related quantities

摘要

The accuracy of the Darcy velocity, flux, and stream function computed from lowest‐order, triangle‐based, control volume and mixed finite element approximations to the two‐dimensional pressure equation is considered. The control volume finite element method, similar to integrated finite difference methods and analogous to the interpolation of Galerkin finite element results over “control volumes,” is shown to yield a conservative velocity field and smooth streamlines. The streamlines and fluxes through the system computed with the control volume finite element approach are compared to those computed from the mixed finite element method, which approximates the pressure and velocity variables separately. It is shown that for systems with only moderate degrees of heterogeneity, the control volume finite element method is the more computationally efficient alternative; i.e., it provides more accurate flow results for a given number of unknowns. For more variable or discontinuous permeability fields, by contrast, such as sand/shale systems, the mixed finite element method is shown to approximate flow variables more accurately and more realistically than the control volume method with the same number of