REGULARITY OF THE DIFFUSION-DISPERSION TENSOR AND ERROR ANALYSIS OF GALERKIN FEMS FOR A POROUS MEDIUM FLOW

摘要

We study Galerkin finite element methods for an incompressible miscible flow in porous media with the commonly used Bear-Scheidegger diffusion-dispersion tensor D(u) = Phi d(m)I+ vertical bar u vertical bar(alpha I-T + (alpha(L) - alpha T)(vertical bar u vertical bar 2)(u circle times u)). The traditional approach to optimal L infinity((0, T); L-2) error estimates is based on an elliptic Ritz projection, which usually requires the regularity of del(x)partial derivative D-t(u(x, t)) is an element of L-p(Omega(T)). However, the Bear-Scheidegger diffusion-dispersion tensor may not satisfy the regularity condition even for a smooth velocity field u. A new approach is presented in this paper, in terms of a parabolic projection, which only requires the Lipschitz continuity of D(u). With the new approach, we establish optimal L-p error estimates and an almost optimal L-infinity error estimate.