What does this research mean for the field?

Novel a posteriori error indicators and an adaptive mesh refinement strategy for a nonlinear least-squares solver effectively guide mesh refinement and scale appropriately for solving the Monge-Ampère equation. Novelty: ClaimNovelty.METHODOLOGICAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

To develop and evaluate novel a posteriori error indicators and an adaptive mesh refinement scheme for a nonlinear least-squares solver applied to the Monge-Ampère equation.

September 5, 2026Journal of Scientific ComputingOpen Access

Error Indicators and Adaptivity for a Least-Squares Method Applied to the Monge-Ampère Equation

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Authors

ACAlexandre CaboussatHong Kong Baptist University APAnna PerusoHES-SO Genève MPMarco PicassoCentre National de la Recherche Scientifique

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Implication

Numerical analysis demonstrates effective adaptive mesh refinement for the Monge-Ampère equation via least-squares error estimators, suggesting improved accuracy for complex geometric solvers.

Key Points

To develop and evaluate novel a posteriori error indicators and an adaptive mesh refinement scheme for a nonlinear least-squares solver applied to the Monge-Ampère equation.
Decoupled the iterative solver into a pointwise nonlinear minimization problem and a linear biharmonic variational problem on convex polygonal 2D domains.
Mapped the biharmonic problem to an equivalent system with Navier boundary conditions and discretized it using mixed piecewise-linear finite elements.
Derived a priori and a posteriori finite element error estimators to drive an adaptive mesh refinement algorithm evaluated on smooth and nonsmooth benchmark tests.
Error norms across both smooth and nonsmooth numerical test cases scaled according to theoretical convergence predictions.
The newly formulated a posteriori error indicators reliably guided local mesh refinement toward regions of high error, confirming the method's adaptivity and robustness.

Cite This Study

Caboussat et al. (2026) studied this question.

synapsesocial.com/papers/6a9bd3e16b95aff0620eb0a8 https://doi.org/10.1007/s10915-026-03435-0

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Implication

Numerical analysis demonstrates effective adaptive mesh refinement for the Monge-Ampère equation via least-squares error estimators, suggesting improved accuracy for complex geometric solvers.

Error Indicators and Adaptivity for a Least-Squares Method Applied to the Monge-Ampère Equation

Discussion

Member takes

Implication

Key Points

Cite This Study

Error Indicators and Adaptivity for a Least-Squares Method Applied to the Monge-Ampère Equation

Discussion

Member takes

Implication

Key Points

Cite This Study

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