Selected aspects of constrained conforming approximation in higher-order FEM

This paper responds to numerous questions and inquiries related to constrained approximation (approximation with hanging nodes) in higher-order finite element methods that we received during the ESCO 2022 conference. We discuss explicit constraints enforced on linear algebra level as well as implici...

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Bibliographic Details
Published inJournal of computational and applied mathematics Vol. 427; p. 115118
Main Authors Solin, Pavel, Cerveny, Jakub
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.08.2023
Subjects
Conforming approximation
Finite element method
Hanging nodes
Irregular mesh
Finite element method
Irregular mesh
Conforming approximation
Hanging nodes
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Summary:This paper responds to numerous questions and inquiries related to constrained approximation (approximation with hanging nodes) in higher-order finite element methods that we received during the ESCO 2022 conference. We discuss explicit constraints enforced on linear algebra level as well as implicit constraints which are built into the basis functions of the finite element space, and selected additional mathematical and algorithmic aspects of conforming higher-order finite element approximations with one-level and arbitrary-level hanging nodes.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2023.115118