一种求解线弹性问题的无闭锁低阶虚拟元方法

A Low-Order Locking-Free Virtual Element Method for the Linear Elasticity Problem

研究了二维区域上线弹性问题的低阶虚拟元方法.用不连续的分段线性向量值函数增扩低阶协调虚拟元空间来构造离散空间,设计了一种离散方法,证明了能量范数下的误差是最优收敛的,和Lamé常数λ无关.最后给出数值算例验证了理论结果.

In this paper,we propose a low-order virtual element method for the linear elasticity problem in two dimensions.We construct a discrete space by enriching the low order conforming virtual element space with discontinuous piecewise linear vector-valued functions.A corresponding discrete problem is introduced.It is proved that the error estimation is optimal with respect to the energy norm,and the hidden constant is independent of the Laméconstantλ.Finally,some numerical examples are given to verify the theoretical results.