Lower-order errors downstream of a shock layer have been detected in computations with nonconstant solutions when using higher-order shock capturing schemes in one and two dimensions [B. Engquist and B. Sjögreen, {SIAM J. Numer. Anal., 35 (1998), pp. 2464--2485].By analyzing the steady-state solution of slightly viscous hyperbolic systems of conservation laws we find that the solution can have an O(h)-dependence downstream of a shock layer, although the viscous term in that region is of O(h²). Numerical examples illustrate the analysis.
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Efraimsson et al. (1999) studied this question.
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