Energy Estimates for Nonlinear Conservation Laws with Applications to Solutions of the Burgers Equation and One-Dimensional Viscous Flow in a Shock Tube by Central Difference Schemes

Abstract

This work revisits an idea that dates back to the early days of scientific computing, the energy method for stability analysis. It is shown that if the scalar non-linear conservation law ∂u ∂t + ∂ ∂x f(u) = 0 is approximated by the semi-discrete conservative scheme duj dt + 1 ∆x ( fj+ 1 2 − fj− 1 2 ) = 0 then the energy of the discrete solution evolves at exactly the same rate as the energy of the true solution, provided that the numerical flux is evaluated by the formula

7 Figures and Tables

Cite this paper

@inproceedings{Jameson2007EnergyEF, title={Energy Estimates for Nonlinear Conservation Laws with Applications to Solutions of the Burgers Equation and One-Dimensional Viscous Flow in a Shock Tube by Central Difference Schemes}, author={Antony Jameson}, year={2007} }