# Maximum principle preserving space and time flux limiting for Diagonally Implicit Runge-Kutta discretizations of scalar convection-diffusion equations

@article{Luna2021MaximumPP, title={Maximum principle preserving space and time flux limiting for Diagonally Implicit Runge-Kutta discretizations of scalar convection-diffusion equations}, author={Manuel Quezada de Luna and David I. Ketcheson}, journal={ArXiv}, year={2021}, volume={abs/2109.08272} }

We provide a framework for high-order discretizations of nonlinear scalar convection-diffusion equations that satisfy a discrete maximum principle. The resulting schemes can have arbitrarily high order accuracy in time and space, and can be stable and maximum-principle-preserving (MPP) with no step size restriction. The schemes are based on a two-tiered limiting strategy, starting with a high-order limiter-based method that may have small oscillations or maximum-principle violations, followed…

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