»ã±¨±êÌâ (Title)£ºSpectral-Galerkin Methods for the Fully Nonlinear Monge-Amp¨¨re Equation

»ã±¨ÈË (Speaker)£ºÀîÕÑÏé ½ÌÊÚ£¨ÉϺ£Ê¦·¶´óѧ£©

»ã±¨¹¦·ò (Time)£º2025Äê10ÔÂ28ÈÕ(Öܶþ) 13:00

»ã±¨µØÖ· (Place)£ºÐ£±¾²¿GJ303

Ô¼ÇëÈË(Inviter)£ºÀƷ¡¢²ÌÃô

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»ã±¨ÌáÒª£ºIn this talk, we develop two numerical methods, namely, the Legendre-Galerkin method and the generalized Log orthogonal functions Galerkin method for numerically solving the fully nonlinear Monge-Amp¨¨re equation. Both methods are constructed based on the vanishing moment approach. To address both solution stability and computational efficiency, we propose a multiple-level framework for resolving discretization schemes. The mathematical justifications of the new approaches and the error estimates for the Legendre-Galerkin method are established. Numerical experiments validate the accuracy of our methods, and a comparative experiment demonstrates the advantage of Log orthogonal functions for problems with corner singularities. The results highlight that our methods have high-order accuracy and small computational cost.