论文标题
液晶聚合物网络膜模型的收敛性FEM
Convergent FEM for a membrane model of liquid crystal polymer networks
论文作者
论文摘要
我们为液晶聚合物网络（LCN）的膜模型设计了有限元方法（FEM）。该模型由非凸伸拉伸能量的最小化问题组成。我们讨论了这种能量功能的特性，例如缺乏弱较低的半持续性。我们通过正则化设计了一个离散化，提出了一种新的迭代方案，以解决非凸口离散最小化问题，并证明了该方案的稳定性和离散最小化器的收敛性。我们提出数值模拟，以说明算法的收敛属性和模型的特征。
We design a finite element method (FEM) for a membrane model of liquid crystal polymer networks (LCNs). This model consists of a minimization problem of a non-convex stretching energy. We discuss properties of this energy functional such as lack of weak lower semicontinuity. We devise a discretization with regularization, propose a novel iterative scheme to solve the non-convex discrete minimization problem, and prove stability of the scheme and convergence of discrete minimizers. We present numerical simulations to illustrate convergence properties of our algorithm and features of the model.
