Standard finite elements for the numerical resolution of the elliptic Monge-Ampere equation: mixed methods
arXiv:1406.5666
Originality Incremental advance
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Provides a theoretical convergence guarantee for a numerical method solving a challenging nonlinear PDE, benefiting computational mathematics and applied fields.
The authors prove convergence of a mixed finite element method for the elliptic Monge-Ampere equation to its weak solution in the sense of Aleksandrov, using unknowns for the scalar variable and Hessian matrix.
We prove a convergence result for a mixed finite element method for the Monge-Ampere equation to its weak solution in the sense of Aleksandrov. The unknowns in the formulation are the scalar variable and the Hessian matrix.