OPTIMIZATION APPROACH FOR THE MONGE-AMPÈRE EQUATION

doi:10.1016/S0252-9602(18)30814-2

摘要/Abstract

摘要：

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.

关键词: elliptic Monge-Ampère equation, gradient conjugate method, finite element Galerkin method

Abstract:

Key words: elliptic Monge-Ampère equation, gradient conjugate method, finite element Galerkin method

Fethi BEN BELGACEM. OPTIMIZATION APPROACH FOR THE MONGE-AMPÈRE EQUATION[J]. 数学物理学报(英文版), 2018, 38(4): 1285-1295.

Fethi BEN BELGACEM. OPTIMIZATION APPROACH FOR THE MONGE-AMPÈRE EQUATION[J]. Acta mathematica scientia,Series B, 2018, 38(4): 1285-1295.

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