地点：新主楼E1114
Title: The ultra-weak local discontinuous Galerkin (UWLDG) method for PDEs with high order spatial derivatives
Abstract: In this talk, we will introduce the UWLDG (Ultra-weak local discontinuous Galerkin) method for PDEs with high order spatial derivatives. We prove the stability of our method in the general nonlinear case and provide optimal error estimates for linear PDEs for the solution itself as well as for the auxiliary variables approximating its derivatives. A key ingredient in the proof of the error estimates is the construction of the relationship between the derivative and the element interface jump of the numerical solution and the auxiliary variable solution of the solution derivative. With this relationship, we can use the discrete Sobolev and Poincare inequalities to obtain the optimal error estimates. Some superconvergence properties of the UWLDG method for high order equations will also be presented.
报告人简介：陶琪，北京工业大学理学部副教授。于2020年获得中国科学技术大学博士学位。2018年至2020年在美国布朗大学应用数学系联合培养。2020年至2022年在北京计算科学研究中心做博士后。2022年加入北京工业大学，入选北京工业大学高层次人才计划。主要研究领域为间断有限元方法的理论分析及应用。在SIAM J. Numer. Anal., Math. Comp., J. Sci. Comput. 等国际期刊发表学术论文十余篇。曾获中国博士后基金特别资助和面上资助，现主持国家自然科学基金青年项目。
科技处 理学院
2024年8月3日