Convergence of a finite volume scheme for nonlinear degenerate parabolic equations

@article{Eymard2002ConvergenceOA,
  title={Convergence of a finite volume scheme for nonlinear degenerate parabolic equations},
  author={Robert Eymard and Thierry Gallou{\"e}t and Rapha{\`e}le Herbin and Anthony Michel},
  journal={Numerische Mathematik},
  year={2002},
  volume={92},
  pages={41-82}
}
We propose a second order finite volume scheme for nonlinear degenerate parabolic equations. For some of these models (porous media equation, drift-diffusion system for semiconductors, ...) it has been proved that the transient solution converges to a steady-state when time goes to infinity. The present scheme preserves steady-states and provides a satisfying long-time behavior. Moreover, it remains valid and second-order accurate in space even in the degenerate case. After describing the… CONTINUE READING
Highly Influential
This paper has highly influenced 10 other papers. REVIEW HIGHLY INFLUENTIAL CITATIONS