A total variation diminishing-projection method for solving implicit numerical schemes for scalar conservation laws: a numerical study of a simple case

Abstract

The stability of Newton’s method applied to implicit numerical schemes for scalar conservation laws requires, in the general case, an upper bound on the size of the timesteps. A simple locally defined projection, a total variation diminishing (TVD)-projection, is introduced, and it is used to obtain always-stable extensions of Newton’s method. A numerical study of this method applied to Godunov’s implicit scheme is presented.