A differentiable mapping of mesh cells based on finite elements on quadrilateral and hexahedral meshes

• Verfasst von: Arndt, Daniel [VerfasserIn]
• Verfasst von: Kanschat, Guido [VerfasserIn]
• Titel: A differentiable mapping of mesh cells based on finite elements on quadrilateral and hexahedral meshes
• Verf.angabe: Daniel Arndt and Guido Kanschat
• Jahr: 2021
• Umfang: 11 S.
• Fussnoten: Gesehen am 05.02.2021
• Titel Quelle: Enthalten in: Computational methods in applied mathematics
• Ort Quelle: Berlin : De Gruyter, 2001
• Jahr Quelle: 2021
• Band/Heft Quelle: 21(2021), 1, Seite 1-11
• ISSN Quelle: 1609-9389
• DOI: doi:10.1515/cmam-2020-0159
• Datenträger: Online-Ressource
• Sprache: eng
• K10plus-PPN: 1747633542

Abstract

Finite elements of higher continuity, say conforming in H 2 instead of H 1, 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.