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High order accurate weighted essentially non-oscillatory (WENO) schemes are usually designed to solve hyperbolic conservation laws or to discretize the first derivative convection terms in convection dominated partial differential equations. In this paper we discuss a high order WENO finite difference discretization for nonlinear degenerate parabolic equations which may contain discontinuous solutions. A porous medium equation is used as an example to demonstrate the algorithm structure anddoi:10.1137/100791002 fatcat:lelpqpmgkzdwfdfzo6iiruleoi