SIAM Journal on Numerical Analysis, Volume 61, Issue 6, Page 2887-2916, December 2023.
Abstract. We design a finite element method for a membrane model of liquid crystal polymer networks. This model consists of a minimization problem of a nonconvex 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 nonconvex 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.

中文翻译：

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液晶聚合物网络膜模型的收敛有限元法

《SIAM 数值分析杂志》，第 61 卷，第 6 期，第 2887-2916 页，2023 年 12 月。
摘要。我们设计了液晶聚合物网络膜模型的有限元方法。该模型由非凸拉伸能量的最小化问题组成。我们讨论该能量泛函的性质，例如缺乏弱下半连续性。我们设计了带有正则化的离散化，提出了一种新颖的迭代方案来解决非凸离散最小化问题，并证明了该方案的稳定性和离散最小化器的收敛性。我们提出数值模拟来说明我们的算法的收敛特性和模型的特征。