A Lax-Wendroff type theorem for unstructured quasi-uniform grids |
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Authors: | Volker Elling. |
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Affiliation: | Division of Applied Mathematics, Brown University, 182 George Street, Providence, Rhode Island 02906 |
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Abstract: | A well-known theorem of Lax and Wendroff states that if the sequence of approximate solutions to a system of hyperbolic conservation laws generated by a conservative consistent numerical scheme converges boundedly a.e. as the mesh parameter goes to zero, then the limit is a weak solution of the system. Moreover, if the scheme satisfies a discrete entropy inequality as well, the limit is an entropy solution. The original theorem applies to uniform Cartesian grids; this article presents a generalization for quasi-uniform grids (with Lipschitz-boundary cells) uniformly continuous inhomogeneous numerical fluxes and nonlinear inhomogeneous sources. The added generality allows a discussion of novel applications like local time stepping, grids with moving vertices and conservative remapping. A counterexample demonstrates that the theorem is not valid for arbitrary non-quasi-uniform grids. |
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Keywords: | Finite volume method conservation law convergence Lax--Wendroff conservative remapping |
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