Articles

OPTIMIZATION APPROACH FOR THE MONGE-AMPÈRE EQUATION

  • Fethi BEN BELGACEM
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  • Department of Mathematics, Laboratoire EDP(LR03ES04), Faculty of Sciences of Tunis, 1060 Tunis, Tunisia

Received date: 2016-09-12

  Revised date: 2018-03-12

  Online published: 2018-08-25

Abstract

In this paper, we introduce and study a method for the numerical solution of the elliptic Monge-Ampère equation with Dirichlet boundary conditions. We formulate the Monge-Ampère equation as an optimization problem. The latter involves a Poisson Problem which is solved by the finite element Galerkin method and the minimum is computed by the conjugate gradient algorithm. We also present some numerical experiments.

Cite this article

Fethi BEN BELGACEM . OPTIMIZATION APPROACH FOR THE MONGE-AMPÈRE EQUATION[J]. Acta mathematica scientia, Series B, 2018 , 38(4) : 1285 -1295 . DOI: 10.1016/S0252-9602(18)30814-2

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