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

Gerard Awanou; Romeo Awi

doi:10.1007/s10440-016-0041-x

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

Gerard Awanou, Romeo Awi

Institute for Mathematics and its Applications

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

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.

Original language	English (US)
Pages (from-to)	87-98
Number of pages	12
Journal	Acta Applicandae Mathematicae
Volume	144
Issue number	1
DOIs	https://doi.org/10.1007/s10440-016-0041-x
State	Published - Aug 1 2016

Bibliographical note

Publisher Copyright:
© 2016, Springer Science+Business Media Dordrecht.

Keywords

Aleksandrov solution
Discrete Monge-Ampère
Weak convergence of measures

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10.1007/s10440-016-0041-x

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abstract = "We present a technique for proving convergence to the Aleksandrov solution of the Monge-Amp{\`e}re 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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KW - Weak convergence of measures

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

Abstract

Bibliographical note

Keywords

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