Standard finite elements for the numerical resolution of the elliptic Monge-Ampere equation: mixed methods
Gerard Awanou
TL;DR
This paper proves convergence of a mixed finite element method for solving the elliptic Monge-Ampere equation, involving scalar and Hessian unknowns, to its weak Aleksandrov solution.
Contribution
It introduces a mixed finite element approach for the Monge-Ampere equation and establishes its convergence to the weak solution.
Findings
Convergence proof for the mixed finite element method.
Validation of the method's effectiveness for the Monge-Ampere equation.
Theoretical foundation for numerical approximation of the equation.
Abstract
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.
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Taxonomy
TopicsGeometry and complex manifolds · Geometric Analysis and Curvature Flows · Nonlinear Partial Differential Equations