汇报标题 (Title)：Spectral-Galerkin Methods for the Fully Nonlinear Monge-Ampère Equation
汇报人 (Speaker)：李昭祥 教授（上海师范大学）
汇报功夫 (Time)：2025年10月28日(周二) 13:00
汇报地址 (Place)：校本部GJ303
约请人(Inviter)：李常品、蔡敏
主办部门：理学院数学系
汇报提要：In 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-Ampère 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.
