发表机构
Monash University; Universidad Adventista de Chile; Indian Institute of Space Science and Technology; Birla Institute of Technology and Science, Pilani（莫纳什大学; 智利基督复临安息日会大学; 印度空间科学技术研究所; 比拉理工与科学学院（皮拉尼校区））
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文采用协调虚拟元方法结合Crank--Nicolson格式求解Kelvin--Voigt黏弹性模型，建立适定性并推导先验误差估计，数值算例验证了方法的有效性。
AI 中文摘要
考虑到虚拟元方法（VEM）的计算优势，本文采用协调虚拟元方法对Kelvin--Voigt黏弹性模型进行数值逼近。为清晰和简洁起见，我们聚焦于原始形式。空间离散采用虚拟元方法，时间离散采用二阶Crank--Nicolson格式。我们建立了半离散和全离散问题的适定性，并推导了先验误差估计。文中给出了几个代表性数值算例，以验证理论结果并展示所提方法的有效性。
英文摘要
Considering the computational advantages of virtual element methods (VEM), this work employs a conforming VEM for the numerical approximation of the Kelvin--Voigt model of viscoelasticity. For clarity and simplicity, we focus on the primal formulation. The spatial discretization is carried out using the virtual element method, while the temporal discretization is handled via the {second-order Crank--Nicolson} scheme. We establish the well-posedness of both the semi-discrete and fully discrete problems and derive {\it a priori} error estimates. Several representative numerical examples are presented to validate the theoretical results and to demonstrate the effectiveness of the proposed formulation.
