We want to propose a new discretization ansatz for the second order Hessian complex exploiting benefits of isogeometric analysis, namely the possibility of high-order convergence and smoothness of test functions. Although our approach is firstly only valid in domains that are obtained by affine linear transformations of a unit cube, we see in the approach a relatively simple way to obtain inf-sup stable and arbitrary fast convergent methods for the underlying Hodge-Laplacians. Background for this is the theory of Finite Element Exterior Calculus (FEEC) which guides us to structure-preserving discrete sub-complexes.

中文翻译：

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基于样条空间的Hessian复形保结构离散化

我们想利用等几何分析的优点，即测试函数的高阶收敛性和平滑性的可能性，为二阶 Hessian 复数提出一种新的离散化 ansatz。尽管我们的方法首先仅在通过单位立方体的仿射线性变换获得的域中有效，但我们在该方法中看到了一种相对简单的方法来获得 inf-sup 稳定和任意快速收敛方法的底层 Hodge-Laplacians。其背景是有限元外微积分 (FEEC) 理论，它指导我们进行结构保持的离散子复合体。