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Pseudo transient continuation and time marching methods for Monge-Ampère type equations

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Abstract

We present two numerical methods for the fully nonlinear elliptic Monge-Ampère equation. The first is a pseudo transient continuation method and the second is a pure pseudo time marching method. The methods are proven to converge to a strictly convex solution of a natural discrete variational formulation with C 1 conforming approximations. The assumption of existence of a strictly convex solution to the discrete problem is proven for smooth solutions of the continuous problem and supported by numerical evidence for non smooth solutions.

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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

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  1. Gerard Awanou
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Correspondence to Gerard Awanou.

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Communicated by: Ian H. Sloan

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Awanou, G. Pseudo transient continuation and time marching methods for Monge-Ampère type equations. Adv Comput Math 41, 907–935 (2015). https://doi.org/10.1007/s10444-014-9391-y

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  • DOI: https://doi.org/10.1007/s10444-014-9391-y

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