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Convergence of numerical methods for conservation laws. (English) Zbl 0606.65063

Numerical methods for the Euler equations of fluid dynamics, Proc. INRIA Workshop, Rocquencourt/France 1983, 3-13 (1985).
[For the entire collection see Zbl 0596.00018.]
We describe some recent work dealing with the convergence of approximate solutions to hyperbolic conservation laws generated by the viscosity method and by conservative difference schemes. Convergence is established using the compensated compactness method of L. Tartar [Res. Notes Math. 39, 136-212 (1979; Zbl 0437.35004) and NATO ASI Ser., Ser. C 111, 263-285 (1983; Zbl 0536.35003)] and F. Murat [Ann. Sc. Norm. Super. Pisa, Cl. Sci., IV. Ser. 5, 489-507 (1978; Zbl 0399.46022)].

MSC:

65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
35J65 Nonlinear boundary value problems for linear elliptic equations