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

Daniel Arndt, Guido Kanschat

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

Finite elements of higher continuity, say conforming in H2 instead of H1, 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.

Original languageEnglish
Pages (from-to)1-11
Number of pages11
JournalComputational Methods in Applied Mathematics
Volume21
Issue number1
DOIs
StatePublished - Jan 1 2021

Funding

The authors gratefully acknowledge support of DFG through priority program 1648 SPPEXA. Guido Kanschat gratefully acknowledges support by the special program “Numerical Analysis of Complex PDE Models in the Sciences” of the Erwin Schrödinger International Institute for Mathematics and Physics (ESI) at University of Vienna.

Keywords

  • Adaptive Refinement
  • Bogner-Fox-Schmit Element
  • Boundary Layers
  • Finite Elements
  • Smooth Mesh Geometry

Fingerprint

Dive into the research topics of 'A differentiable mapping of mesh cells based on finite elements on quadrilateral and hexahedral meshes'. Together they form a unique fingerprint.

Cite this