论文标题
平面弹性的无稳定偶然性虚拟元素方法
Stabilization-free serendipity virtual element method for plane elasticity
论文作者
论文摘要
我们提出了应用于平面弹性问题的高阶无稳定虚拟元素方法。我们利用一种偶然性方法来减少从相应的高阶近似值中自由度的总数。该问题的适应性通过数值研究，通过特征分析研究。然后将该方法应用于线性弹性中的几个基准问题，我们表明该方法以$ l^2 $ norm和能量符号的最佳收敛速率和能量符号符合理论估计以及来自高阶虚拟元素方法的收敛速率。
We present a higher order stabilization-free virtual element method applied to plane elasticity problems. We utilize a serendipity approach to reduce the total number of degrees of freedom from the corresponding high-order approximations. The well-posedness of the problem is numerically studied via an eigenanalysis. The method is then applied to several benchmark problems from linear elasticity and we show that the method delivers optimal convergence rates in $L^2$ norm and energy seminorm that match theoretical estimates as well as the convergence rates from higher order virtual element methods.
