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This is a Quantitative Study study.

October 3, 2025Open Access

Error estimates and adaptivity for a least-squares method applied to the Monge-Ampère equation

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This work demonstrates a novel least-squares method for solving the Monge-Ampère equation, suggesting effective adaptive mesh refinement strategies.

A posteriori error indicators effectively guide adaptive mesh refinement, improving solution accuracy.
This approach encompasses both nonlinear minimization and biharmonic variational problems, using mixed piecewise-linear finite elements.
Numerical tests reveal that the proposed error estimators scale appropriately across different norms.
The method shows potential in enhancing computational strategies for solving the Monge-Ampère equation on complex domains.

Caboussat et al. (2025) studied this question.

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This work demonstrates a novel least-squares method for solving the Monge-Ampère equation, suggesting effective adaptive mesh refinement strategies.