标题： 关于Sobolev方程（含对流）的虚拟元方法的收敛性分析 显示英文标题

标题： Convergence Analysis of Virtual Element Methods for the Sobolev Equation with Convection

摘要： 我们研究了虚拟单元在求解带有对流项的Sobolev方程中的潜在应用。 采用一致的虚拟单元方法进行空间离散化，同时使用隐式Euler格式来逼近时间导数。为了建立最优收敛率，引入了一种新的中间投影算子。我们讨论并分析了半离散和全离散格式，分别推导出能量范数和L2-范数下的最优误差估计。进行了若干数值实验以验证理论结果，并评估所提出的数值方法的计算效率。 显示英文摘要

摘要： We explore the potential applications of virtual elements for solving the Sobolev equation with a convective term. A conforming virtual element method is employed for spatial discretization, while an implicit Euler scheme is used to approximate the time derivative. To establish the optimal rate of convergence, a novel intermediate projection operator is introduced. We discuss and analyze both the semi-discrete and fully discrete schemes, deriving optimal error estimates for both the energy norm and L2-norm. Several numerical experiments are conducted to validate the theoretical findings and assess the computational efficiency of the proposed numerical methods.