A Differentiable Mapping of Mesh Cells Based on Finite Elements on Quadrilateral and Hexahedral Meshes

Finite elements of higher continuity, say conforming in instead of , require a mapping from reference cells to mesh cells which is continuously differentiable across cell interfaces. In this article, we propose an algorithm to obtain such mappings given a topologically regular mesh in the standard f...

Full description

Saved in:
Bibliographic Details
Published inJournal of computational methods in applied mathematics Vol. 21; no. 1; pp. 1 - 11
Main Authors Arndt, Daniel, Kanschat, Guido
Format Journal Article
LanguageEnglish
Published Minsk De Gruyter 01.01.2021
Walter de Gruyter GmbH
Subjects
65N50
Adaptive Refinement
Algorithms
Bogner–Fox–Schmit Element
Boundary Layers
Finite Elements
Graph theory
Grid refinement (mathematics)
Mapping
Quadrilaterals
Smooth Mesh Geometry
Online AccessGet full text

Cover

More Information
Summary:Finite elements of higher continuity, say conforming in instead of , require a mapping from reference cells to mesh cells which is continuously differentiable across cell interfaces. In this article, we propose an algorithm to obtain such mappings given a topologically regular mesh in the standard format of vertex coordinates and a description of the boundary. A variant of the algorithm with orthogonal edges in each vertex is proposed. We introduce necessary modifications in the case of adaptive mesh refinement with nonconforming edges. Furthermore, we discuss efficient storage of the necessary data.
ISSN:1609-4840
1609-9389
DOI:10.1515/cmam-2020-0159