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arXiv · 2109.05293

Structure-preserving Discretization of the Hessian Complex based on Spline Spaces

Jeremias Arf·Bernd Simeon
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Abstract

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.

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Jeremias Arf, Bernd Simeon. 2021-09-11. Structure-preserving Discretization of the Hessian Complex based on Spline Spaces. https://arxiv.org/abs/2109.05293

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