Monotone and Consistent discretization of the Monge-Ampere operator
Benamou, Jean-David; Collino, Francis; Mirebeau, Jean-Marie (2016), Monotone and Consistent discretization of the Monge-Ampere operator, Mathematics of Computation, 85, p. 2743-2775. 10.1090/mcom/3080
TypeArticle accepté pour publication ou publié
Journal nameMathematics of Computation
American Mathematical Society
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Abstract (EN)We introduce a novel discretization of the Monge-Ampere operator, simultaneously consistent and degenerate elliptic, hence accurate and robust in applications. These properties are achieved by exploiting the arithmetic structure of the discrete domain, assumed to be a two dimensional cartesian grid. The construction of our scheme is simple, but its analysis relies on original tools seldom encountered in numerical analysis, such as the geometry of two dimensional lattices, and an arithmetic structure called the Stern-Brocot tree. Numerical experiments illustrate the method's efficiency.
Subjects / KeywordsMonotone Finite differences scheme; Monge Ampere PDE; Stern-Brocot tree; Lattice Basis reduction
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