The Monge-Amp\`{e}re equation

Understand

We review recent advances in the numerical analysis of the Monge-Amp\`ere equation.

• Various computational techniques are discussed including wide-stencil finite difference schemes, two-scaled methods, finite element methods, and methods based on geometric considerations.
• Particular focus is the development of appropriate stability and consistency estimates which lead to rates of convergence of the discrete approximations.
• Finally we present numerical experiments which highlight each method for a variety of test problem with different levels of regularity.