AN ORDER OF WEAK CONVERGENCE OF NUMERICAL SOLUTIONS TO THE ENTROPY SOLUTION OF A SCALAR CONSERVATION LAW

Abstract

The weak convergence of numerical solutions to the exact entropy solution of a scalar conservation law for the Hopf quasilinear equation has been studied. The upwind and the Lax — Friedrichs numerical methods being respectively the first and the second order approximation on spatial variable were used for the study. The linear functional derived from the Kruzhkov entropy solution definition was computed using series of numerical solutions on dichotomic nested grids to get the estimation of the weak convergence order. It has been shown that the order of weak convergence is lower than one, being independent on the order of approximation of the method

Keywords

• энтропийное решение по Кружкову
• линейный функционал