Properties of the multidimensional finite elements

Petrov, Miroslav S.; Todorov, Todor D.

doi:10.1016/j.amc.2020.125695

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Cited by 5 publications

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“…Moreover, the elements of [ Ŝ10 ] are invariant. For more details concerning this class of pentatopes, we refer the reader to [30].…”

Section: Theoretical Resultsmentioning

confidence: 99%

Enabling four-dimensional conformal hybrid meshing with cubic pyramids

Petrov¹,

Todorov²,

Walters³

et al. 2021

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The main purpose of this article is to develop a novel refinement strategy for four-dimensional hybrid meshes based on cubic pyramids. This optimal refinement strategy subdivides a given cubic pyramid into a conforming set of congruent cubic pyramids and invariant bipentatopes. The theoretical properties of the refinement strategy are rigorously analyzed and evaluated. In addition, a new class of fully symmetric quadrature rules with positive weights are generated for the cubic pyramid. These rules are capable of exactly integrating polynomials with degrees up to 12. Their effectiveness is successfully demonstrated on polynomial and transcendental functions. Broadly speaking, the refinement strategy and quadrature rules in this paper open new avenues for four-dimensional hybrid meshing, and space-time finite element methods.Keywords 4D hybrid meshes • cubic pyramids • bipentatopes • pentatopes • optimal refinement strategy • quadrature

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“…Moreover, the elements of [ Ŝ10 ] are invariant. For more details concerning this class of pentatopes, we refer the reader to [30].…”

Section: Theoretical Resultsmentioning

confidence: 99%