报 告 人：王天军
报告题目：Legendre Spectral Method For Solving Neumann Boundary Value Problems
报告时间：2017年12月22日（周五）下午17:00
报告地点：静远楼204报告厅
主办单位：数学与统计学院、科技处
报告人简介：
王天军教授，河南科技大学数学与统计学院副院长，长期从事偏微分方程数值方法的研究工作，在《Math. Comp.》、《Adv. in Comp. Math.》、《J. Sci. Comput.》、《Appl. Numer. Math.》以及《Comm. Comp. Phys.》等国际著名学术期刊上发表论文20多篇。主持和承担国家自然科学基金面上项目5项，博士论文获2009年全国百篇优秀博士论文提名奖和上海市优秀博士论文奖。
报告摘要：
In this talk, we consider Neumann boundary value problems on rectangle,cube or quadrilaterals. The algorithm was firstly proposed by Auteri,Parolini and Quartapelle. This method differs from the classicalspectral methods for Neumann boundary value problems. The homogeneousboundary condition is satisfied exactly. Moreover, a double diagonalization processis employed, instead of the full stiffness matrices encountered inthe classical variational formulation of the problem with aweak natural imposition of the derivative boundarycondition. Nonhomogeneous Neumann data is accounted for by means of alifting. In particular, the lifting is expressed explicitly and isdifferent from that in work of Auteri, Parolini and Quartapelle. Foranalyzing the numerical errors, some basic results on Legendre quasi-orthogonaland orthogonal approximations are established. Theconvergences of proposed schemes are proved.Numerical results demonstrate the efficiency of this approachand coincide well with theoretical analysis.
