Convergent filtered scheme for the Monge-Ampère Equation
Abstract
We propose an extension to our monotone and convergent method for the Monge-Ampère equation in dimension d ≥2, that incorporates the idea of filtered schemes. The method combines our original monotone operator with a more accurate non-monotone modification, using an appropriately chosen filter. This results in a remarkable improvement of accuracy, but without sacrificing the convergence to the unique viscosity solution.
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