A general formulation of the Euler characteristic Galerkin (ECG) technique is given for scalar conservation laws, from which specific algorithms are derived and analysed. These are developed from piecewise constant approximations. The basic first-order scheme is then Brenier’s extension of the Engquist–Osher method; but adaptive recovery techniques are used to resolve discontinuities accurately and give second-order accuracy for smooth flows. Convergence is proved for convex flux functions, nonuniform meshes, and arbitrary timesteps, under conditions that can be readily met by the recovery procedures.
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Childs et al. (1990) studied this question.
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