no. 3
High order approximation of Hodge Laplace problems with local coderivatives on cubical meshes
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 56 (2022) no. 3, pp. 867-891

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.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1051/m2an/2022009
Classification : 65N30
Keywords: Perturbed mixed methods, local constitutive laws 
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     title = {High order approximation of {Hodge} {Laplace} problems with local coderivatives on cubical meshes},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {867--891},
     year = {2022},
     publisher = {EDP-Sciences},
     volume = {56},
     number = {3},
     doi = {10.1051/m2an/2022009},
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     language = {en},
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Lee, Jeonghun J. High order approximation of Hodge Laplace problems with local coderivatives on cubical meshes. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 56 (2022) no. 3, pp. 867-891. doi: 10.1051/m2an/2022009

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