反平面剪切松弛细观连续体模型的混合H1xH（旋度）有限元列式
A hybrid H1xH(curl) finite element formulation for a relaxed micromorphic continuum model of antiplane shear
摘要：
模拟超材料的一种方法是扩展与其运动学方程相关的连续介质理论，弛豫微态连续介质就是这样一种模型。它结合了卷曲的非对称微观失真的自由能函数。这表明存在不属于H1的解，使得标准节点H1有限元产生不令人满意的收敛速度，并且可能无法找到精确解。我们的方法是使用来自希尔伯特空间H1和H（旋度）的基函数，展示了此类组合对这类问题的核心作用。为了简单起见，一个减少的二维松弛微观连续描述反平面剪切，保留了三维版本的主要计算特征。然后，该模型用于制定和一个可行的有限元解决方案的多步调查，包括考试的存在性和唯一性的标准和混合配方及其各自的收敛速度。
英文摘要：
One approach for the simulation of metamaterials is to extend an associated continuum theory concerning its kinematic equations, and the relaxed micromorphic continuum represents such a model. It incorporates the Curl of the nonsymmetric microdistortion in the free energy function. This suggests the existence of solutions not belonging to H1, such that standard nodal H1-finite elements yield unsatisfactory convergence rates and might be incapable of finding the exact solution. Our approach is to use base functions stemming from both Hilbert spaces H1 and H(curl), demonstrating the central role of such combinations for this class of problems. For simplicity, a reduced two-dimensional relaxed micromorphic continuum describing antiplane shear is introduced, preserving the main computational traits of the three-dimensional version. This model is then used for the formulation and a multi step investigation of a viable finite element solution, encompassing examinations of existence and uniqueness of both standard and mixed formulations and their respective convergence rates.
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