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Convergent Semi-Lagrangian Methods for the Monge--Ampère Equation on Unstructured Grids
This paper is concerned with developing and analyzing convergent semi-Lagrangian methods for the fully nonlinear elliptic Monge--Ampère equation on general triangular grids. This is done by establishing an equivalent (in the viscosity sense) Hamilton--Jacobi--Bellman formulation of the Monge--Ampère equation. A significant benefit of the reformulation is the removal of the …