报告题目： Superconvergence of the local discontinuous Galerkin method for nonlinear convection-diffusion equations
报 告 人：孟雄
工作单位：哈尔滨工业大学
报告时间：2023-06-08 8:30-10:30
腾讯会议ID： 553-743-115
报告摘要：In this talk, we present superconvergence properties of the local discontinuous Galerkin (LDG) methods for solving nonlinear convection-diffusion equations in one space dimension. The main technicality is an elaborate estimate to terms involving projection errors. By introducing a new projection and constructing some correction functions, we prove the (2k+1)th order superconvergence for the cell averages and the numerical flux in the discrete L2 norm with polynomials of degree k≥1, no matter whether the flow direction f'(u) changes or not. Superconvergence of order k +2 (k +1) is obtained for the LDG error (its derivative) at interior right (left) Radau points, and the convergence order for the error derivative at Radau points can be improved to k+2 when the direction of the flow doesn't change. Finally, a supercloseness result of order k+2 towards a special Gauss-Radau projection of the exact solution is shown. The superconvergence analysis can be extended to the generalized numerical fluxes and the mixed boundary conditions. All theoretical findings are confirmed by numerical experiments.
报告人简介：
孟雄，哈尔滨工业大学数学学院教授、博导、省优青，欧盟玛丽居里学者、美国布朗大学访问学者，主要研究方向为计算流体力学间断有限元方法的设计、分析与应用。在SIAM Journal on Numerical Analysis, Numerische Mathematik, Mathematics of Computation等期刊发表论文16篇。主持欧盟“玛丽居里行动”计划基金、国家自然科学基金面上项目、国家自然科学基金青年基金等项目。获中国工业与应用数学学会应用数学青年科技奖和国家天元数学东北中心优秀青年学者等奖励。
