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Numerical methods for flows through porous media. I

Author: Michael E. Rose
Journal: Math. Comp. 40 (1983), 435-467
MSC: Primary 65M60; Secondary 76S05
MathSciNet review: 689465
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Abstract: The degenerate parabolic equation

$\displaystyle \frac{{\partial u}}{{\partial t}} = \nabla \cdot \left( {\vert u{\vert^\nu }\nabla u} \right),\quad \nu \geqslant 1,$

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.

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