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 language | English |
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Pages (from-to) | 1-11 |
Number of pages | 11 |
Journal | Computational Methods in Applied Mathematics |
Volume | 21 |
Issue number | 1 |
DOIs | |
State | Published - 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