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Convergence Rate for the Ordered Upwind Method

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Abstract

The ordered upwind method (OUM) is used to approximate the viscosity solution of the static Hamilton–Jacobi–Bellman with direction-dependent weights on unstructured meshes. The method has been previously shown to provide a solution that converges to the exact solution, but no convergence rate has been theoretically proven. In this paper, it is shown that the solutions produced by the OUM in the boundary value formulation converge at a rate of at least the square root of the largest edge length in the mesh in terms of maximum error. An example with similar order of numerical convergence is provided.

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Authors and Affiliations

  1. University of Waterloo, Waterloo, Canada

    Alex Shum, Kirsten Morris & Amir Khajepour

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  1. Alex Shum
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  2. Kirsten Morris
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  3. Amir Khajepour
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Correspondence to Alex Shum.

Additional information

This work has been supported by the Ontario Government, and Natural Sciences and Engineering Research Council.

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Shum, A., Morris, K. & Khajepour, A. Convergence Rate for the Ordered Upwind Method. J Sci Comput 68, 889–913 (2016). https://doi.org/10.1007/s10915-016-0163-3

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  • DOI: https://doi.org/10.1007/s10915-016-0163-3

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