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A posteriori error estimates for general numerical methods for scalar conservation laws. (English) Zbl 0834.65091
The authors consider the conservation law for \(v(t,x)\) defined by \(\partial v/\partial t + \nabla f (v) = 0\), \(0 < t < T\), \(v(0,x) = v_0(x)\), (\(\nabla\) and \(f\) are considered as being of an arbitrary number of dimensions). They produce an approximating process for the solution of this problem, and evaluate the associated error estimate. The estimate is independent of the number of dimensions and of the nature of the nonlinearity of \(f\).
Tables of the results of numerical calculations for some particular types of \(f\) and various values for \(T\) obtained by the use of the Engquist- Osher scheme are given.

MSC:
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35L65 Hyperbolic conservation laws
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