Volume 56, Number 3, May-June 2022
|867 - 891
|25 April 2022
High order approximation of Hodge Laplace problems with local coderivatives on cubical meshes
Department of Mathematics, Baylor University, Waco, TX, USA
* Corresponding author: email@example.com
Accepted: 17 January 2022
In mixed finite element approximations of Hodge Laplace problems associated with the de Rham complex, the exterior derivative operators are computed exactly, so the spatial locality is preserved. However, the numerical approximations of the associated coderivatives are nonlocal and can be regarded as an undesired effect of standard mixed methods. For numerical methods with local coderivatives, a perturbation of low order mixed methods in the sense of variational crimes has been developed for simplicial and cubical meshes. In this paper we extend the low order method to all high orders on cubical meshes using a new family of finite element differential forms on cubical meshes. The key theoretical contribution is a generalization of the linear degree, in the construction of the serendipity family of differential forms, and this generalization is essential in the unisolvency proof of the new family of finite element differential forms.
Mathematics Subject Classification: 65N30
Key words: Perturbed mixed methods / local constitutive laws
© The authors. Published by EDP Sciences, SMAI 2022
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