粘弹性方程全离散化有限体积元格式及数值模拟

A FULLY DISCRETE FINITE VOLUME ELEMENT FORMULATION AND NUMERICAL SIMULATIONS FOR VISCOELASTIC EQUATIONS

本文利用有限体积元方法研究二维粘弹性方程,给出一种时间二阶精度的全离散化有限体积元格式,并给出这种全离散化有限体积元解的误差估计,最后用数值例子验证数值结果与理论结果是相吻合的.通过与有限元方法和有限差分方法相比较,进一步说明了全离散化有限体积元格式是求解二维粘弹性方程数值解的最有效方法之一.

In this paper, two-dimensional （2D） viscoelastic equations are studied with a finite volume element （FVE） method, a fully discrete finite volume element formulation with second order time accuracy is established, and the error estimates of the discrete FVE solutions are provided. A numerical example is used to illustrate the fact that the results of numerical computation are consistent with theoretical conclusions. Moreover, it has shown that the fully discrete FVE formulation is one of the most efficient for finding numerical solutions of 2D viscoelastic equations by comparing with the numerical results of a fully discrete finite element formulation and a finite difference scheme.