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Convergence of Finite Difference Schemes to the Aleksandrov Solution of the Monge-Ampère Equation

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Abstract

We present a technique for proving convergence to the Aleksandrov solution of the Monge-Ampère equation of a stable and consistent finite difference scheme. We also require a notion of discrete convexity with a stability property and a local equicontinuity property for bounded sequences.

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Acknowledgements

We would like to thank the referees for a careful reading of the paper. Gerard Awanou was partially supported by a Division of Mathematical Sciences of the US National Science Foundation grant No. 1319640.

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Authors and Affiliations

  1. Department of Mathematics, Statistics, and Computer Science (M/C 249), University of Illinois at Chicago, Chicago, IL, 60607-7045, USA

    Gerard Awanou

  2. IMA, University of Minnesota, 207 Church Street SE, 306 Lind Hall, Minneapolis, MN, 55455, USA

    Romeo Awi

Authors
  1. Gerard Awanou
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  2. Romeo Awi
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Correspondence to Gerard Awanou.

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Awanou, G., Awi, R. Convergence of Finite Difference Schemes to the Aleksandrov Solution of the Monge-Ampère Equation. Acta Appl Math 144, 87–98 (2016). https://doi.org/10.1007/s10440-016-0041-x

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  • DOI: https://doi.org/10.1007/s10440-016-0041-x

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