講座主題：Error analysis of spectral method for the Monge-Ampère equation on convex quadrilaterals and hexahedrons
專(zhuān)家姓名：李昭祥
工作單位：上海師范大學(xué)
講座時(shí)間：2026年01月20日 08:30-09:30
講座地點(diǎn)：騰訊會(huì)議：613-795-021
主辦單位：煙臺(tái)大學(xué)數(shù)學(xué)與信息科學(xué)學(xué)院
內(nèi)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.
主講人介紹：
李昭祥，上海師范大學(xué)計(jì)算數(shù)學(xué)專(zhuān)業(yè)教授，博士研究生導(dǎo)師。主要從事譜方法和微分方程多解的數(shù)值方法研究。目前主持國(guó)家自然科學(xué)基金面上項(xiàng)目1項(xiàng)。主持完成上海市自然科學(xué)基金面上項(xiàng)目2項(xiàng)，國(guó)家自然科學(xué)基金面上項(xiàng)目、國(guó)家博士后基金面上項(xiàng)目、上海市教委創(chuàng)新項(xiàng)目和優(yōu)秀青年教師項(xiàng)目各1項(xiàng)，參與多項(xiàng)國(guó)家和省部級(jí)項(xiàng)目。在國(guó)內(nèi)外學(xué)術(shù)期刊上發(fā)表學(xué)術(shù)論文30余篇。
