Efficient implementation of essentially non-oscillatory shock-capturing schemes
Journal of Computational Physics
solution of nonlinear diffusion problems by linear approximation schemes
SIAM Journal on Numerical Analysis
Weighted essentially non-oscillatory schemes
Journal of Computational Physics
Efficient implementation of weighted ENO schemes
Journal of Computational Physics
The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems
SIAM Journal on Numerical Analysis
A posteriori error estimation and adaptivity for degenerate parabolic problems
Mathematics of Computation
Journal of Computational Physics
Journal of Computational Physics
A technique of treating negative weights in WENO schemes
Journal of Computational Physics
Understanding the Shu–Osher Conservative Finite Difference Form
Journal of Scientific Computing
Multidomain WENO Finite Difference Method with Interpolation at Subdomain Interfaces
Journal of Scientific Computing
Explicit diffusive kinetic schemes for nonlinear degenerate parabolic systems
Mathematics of Computation
Mapped weighted essentially non-oscillatory schemes: Achieving optimal order near critical points
Journal of Computational Physics
A Weighted Essentially Nonoscillatory, Large Time-Step Scheme for Hamilton--Jacobi Equations
SIAM Journal on Scientific Computing
Journal of Computational Physics
High-Order Relaxation Schemes for Nonlinear Degenerate Diffusion Problems
SIAM Journal on Numerical Analysis
Journal of Scientific Computing
SIAM Journal on Scientific Computing
A New Nonsymmetric Discontinuous Galerkin Method for Time Dependent Convection Diffusion Equations
Journal of Scientific Computing
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High order accurate weighted essentially nonoscillatory (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 (PME) is used as an example to demonstrate the algorithm structure and performance. By directly approximating the second derivative term using a conservative flux difference, the sixth order and eighth order finite difference WENO schemes are constructed. Numerical examples are provided to demonstrate the accuracy and nonoscillatory performance of these schemes.