论文标题
使用混合和稳定的有限元素进行线性弹性进行攻击
Mortaring for linear elasticity using mixed and stabilized finite elements
论文作者
论文摘要
这项工作的目的是研究使用标准低阶有限元元素空间来研究线性弹性的迫击炮方法。基于残留稳定，我们引入了一种稳定的迫击炮方法，以进行线性弹性，并将其与未稳定的混合砂浆方法进行比较。为简单起见，这两种方法都使用仅从接口的一侧继承的跟踪网格上定义的Lagrange乘法器。我们得出了稳定方法的准典型性估计，并提供了混合$ P_1-P_1 $近似的稳定性标准。我们的数值结果表明了连接接触问题的方法的稳定性和收敛性。此外，结果表明，混合方法可以成功扩展到三维问题。
The purpose of this work is to study mortar methods for linear elasticity using standard low order finite element spaces. Based on residual stabilization, we introduce a stabilized mortar method for linear elasticity and compare it to the unstabilized mixed mortar method. For simplicity, both methods use a Lagrange multiplier defined on a trace mesh inherited from one side of the interface only. We derive a quasi-optimality estimate for the stabilized method and present the stability criteria of the mixed $P_1-P_1$ approximation. Our numerical results demonstrate the stability and the convergence of the methods for tie contact problems. Moreover, the results show that the mixed method can be successfully extended to three dimensional problems.
