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Thierry Buffard Thierry Gallouet and JeanMarc Herard
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1999 Birkhauser Verlag advection equations algorithm Anal approximation assume asymptotic Birkhauser Verlag Basel/Switzerland blowup boundary conditions Cauchy problem characteristic coefficients computed conservation laws consider constant convergence corresponding curve defined delta-shock denote density derivatives detonation differential equations diffusion discontinuity domain E-mail address eigenvalues eikonal equation entropy error estimate Euler equations existence Figure finite flow fluid flux formula function gas dynamics geometric optics grid hyperbolic conservation laws hyperbolic systems initial data integral interface kinetic Lemma level-set limit linear Math matrix mesh method Navier-Stokes equations nonlinear numerical solution obtained one-dimensional Orlicz spaces oscillations perturbation Phys piecewise pressure propagation properties quasi-characteristics relaxation system Riemann problem satisfies second order Sethian shallow water equations shock waves smooth solved source terms space dimensions stability stiff symmetric systems of conservation Theorem thermodynamic third order scheme tion unique upwind variables vector velocity Viscosity Solutions weak solution well-posedness zero