Numerical Methods for Flows Through Porous Media. I

The degenerate parabolic equation \[ \frac {{\partial u}}{{\partial t}} = \nabla \cdot \left ( {|u{|^\nu }\nabla u} \right ),\quad \nu \geqslant 1,\] has been used to model the flow of gas through a porous medium. Error estimates for continuous and discrete time finite element procedures to approximate the solution of this equation are proved, and several new regularity results are given.