粘弹性方程一种新的分裂正定混合元法

A NEW SPLITTING POSITIVE DEFINITE MIXED FINITE ELEMENT METHOD FOR VISCOELASTIC EQUATION

本文用分裂正定混合有限元方法研究二阶粘弹性方程.首先构造一种新的分裂正定混合变分形式和基于这种分裂正定混合变分形式关于时间的半离散格式,然后绕开关于空间变量的半离散化格式,直接从时间半离散出发构造出全离散化的分裂正定混合有限元格式,并给出这种分裂正定混合有限元解的误差估计.这种研究思路使得理论论证变得更简单,这是处理二阶粘弹性方程的一种新的尝试.

In this paper, a second-order viscoelastic equation is studied with a splitting posluve definite mixed finite element method. A new splitting positive definite mixed variational form and a semi-discrete formulation with respect to time based on the splitting positive definite mixed variational form are established first. And then, a fully discrete splitting positive definite mixed finite element formulation is established directly from the semi-discrete formulation with respect to time. Finally, the error estimates of the splitting positive definite mixed finite element solutions are provided. The studied approaches could make theoretical argumentation simpler and more convenient, which is a new study attempt for second-order viscoelastic equation.