讲座主题：Error analysis of spectral method for the Monge-Ampère equation on convex quadrilaterals and hexahedrons

专家姓名：李昭祥

工作单位：上海师范大学

讲座时间：2026年01月20日 08:30-09:30

讲座地点：腾讯会议：613-795-021

主办单位：烟台大学数学与信息科学学院

内容摘要：

In this talk, we investigate a Legendre spectral method for the fully nonlinear Monge-Ampère equation on convex quadrilateral and hexahedral domains. To this end, we first develop several theoretical results on Legendre irrational orthogonal approximations, which play an essential role in extending spectral methods to quadrilateral and hexahedral domains. Based on these results, we develop the Legendre spectral scheme for the Monge-Ampère equation and derive error estimates using linearization and fixed-point arguments. A regularized Newton method is employed to enhance the stability of the iterative procedure. Numerical experiments indicate that the proposed method achieves convergence to the convex viscosity solution and confirm its accuracy and efficiency.

主讲人介绍：

李昭祥，上海师范大学计算数学专业教授，博士研究生导师。主要从事谱方法和微分方程多解的数值方法研究。目前主持国家自然科学基金面上项目1项。主持完成上海市自然科学基金面上项目2项，国家自然科学基金面上项目、国家博士后基金面上项目、上海市教委创新项目和优秀青年教师项目各1项，参与多项国家和省部级项目。在国内外学术期刊上发表学术论文30余篇。