Abstract
In this paper we discuss the issue of conservation and convergence to weak solutions of several global schemes, including the commonly used compact schemes and spectral collocation schemes, for solving hyperbolic conservation laws. It is shown that such schemes, if convergent boundedly almost everywhere, will converge to weak solutions. The results are extensions of the classical Lax–Wendroff theorem concerning conservative schemes.
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Carpenter, M.H., Gottlieb, D. & Shu, CW. On the Conservation and Convergence to Weak Solutions of Global Schemes. Journal of Scientific Computing 18, 111–132 (2003). https://doi.org/10.1023/A:1020390212806
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DOI: https://doi.org/10.1023/A:1020390212806