Hyperbolic Systems of Conservation Laws

3-point apply approximation associated Assume belongs bounded called Chapter 11 classical coefficient computation conservation form conservation laws consider consistent constant construct continuous converges convex corresponding defined definition denote depends derive difference scheme differential discontinuity dx dt E-scheme easy entropy condition entropy solution equation equivalent estimate EXAMPLE exists fact Figure formula function function f given gives Godunov grad hand Hence holds implies incremental inequality initial instance integral interval introduce jump Lemma limit linear method modified monotone Moreover nonlinear Note numerical flux obtain order accurate piecewise preserving Proof Proposition prove refer remains REMARK requirement result Riemann problem satisfies second order sequence shock shows side simple smooth solution of 1.1 space step strictly suppose term Theorem unique values variables viscosity wave weak solution write written yields