Abstract: For the onedimensional porous medium problem, wave front of the numerical solution could not propagate forward when  the standard mixed finite volume element method was used to solve them, we proposed  a new mixed finite volume element method for  solving the degradation problem, in which the  flux variable only included the derivative of the original variable  to spacial variable. The results show that the  method can avoid the phenomenon that wave front of the numerical solution can  not propagate forward, and can capture the interface of numerical solution well. The validity of the  method is verified by numerical experiments.

Key words: porous medium problem, mixed finite volume element method, Picard iteration