Error estimates of serendipity virtual element methods for semilinear parabolic integro-differential equations on curved domains

报告题目：Error estimates of serendipity virtual element methods for semilinear parabolic integro-differential equations on curved domains

主讲人：赵景军教授（哈尔滨工业大学）

时间：2025年7月26日（周六）15:30 p.m.

地点：北院卓远楼305会议室

主办单位：统计与数学学院

摘要：Different from the standard virtual element method, the serendipity virtual element method eliminates all the internal-moment degrees of freedom only under certain conditions of the mesh and the degree of approximation. Consequently, if the interpolation operators are utilized to approximate the nonlinear terms, the implementation of Newton's iteration algorithm can be simplified. The strategy of approximating curved domains with polygonal domains is taken into consideration. To overcome the suboptimal convergence caused by enforcing Dirichlet boundary conditions strongly, Nitsche-based projection method is employed to impose the boundary conditions weakly. For time discretization, Crank-Nicolson scheme incorporating trapezoidal quadrature rule is adopted. Based on Nitsche-based projection method, a Ritz-Volterra projection is introduced and its approximation properties are analyzed. Moreover, error estimates are derived for the fully discrete scheme. Finally, the extension of the fully discrete scheme to 3D case is also included.

主讲人简介：

赵景军，哈尔滨工业大学数学学院教授、博士生导师。哈尔滨工程大学兼职教授、博士生导师。曾访问剑桥大学、阿尔伯塔大学、香港大学、中科院数学与系统科学研究院。现任黑龙江省工业与应用数学学会常务理事。主要从事微分方程数值解的研究。在SIAM J. Numer. Anal.和J. Sci. Comput.等期刊发表SCI论文80余篇，主持和参加国家自然科学基金、国防预研基金多项。先后获中国高校自然科学二等奖、黑龙江省科学技术二等奖。