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.
翻译:这项工作的目的是利用标准低顺序限制元素空间研究线性弹性的迫击炮方法。根据残余稳定度,我们引入了线性弹性稳定迫击炮方法,并将其与不稳定的混合迫击炮方法进行比较。为了简单起见,两种方法都使用仅从界面的一面继承的微小网目上定义的弧度乘数。我们得出了稳定方法的准最佳估计值,并提出了混合的$P_1-P_1美元近似值的稳定性标准。我们的数字结果显示了绑定接触问题方法的稳定性和趋同性。此外,结果还表明混合方法可以成功地扩大到三维问题。