Construction of local $C^1$ quartic spline elements for optimal-order approximation
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- by Charles K. Chui and Dong Hong PDF
- Math. Comp. 65 (1996), 85-98 Request permission
Abstract:
This paper is concerned with a study of approximation order and construction of locally supported elements for the space $S_4^1(\Delta )$ of $C^1$ $pp$ (piecewise polynomial) functions on an arbitrary triangulation $\Delta$ of a connected polygonal domain $\Omega$ in $\Bbb R^2$. It is well known that even when $\Delta$ is a three-directional mesh $\Delta ^{(1)}$, the order of approximation of $S_4^1(\Delta ^{(1)})$ is only 4, not 5. The objective of this paper is two-fold: (i) A local Clough-Tocher refinement procedure of an arbitrary triangulation $\Delta$ is introduced so as to yield the optimal (fifth) order of approximation, where locality means that only a few isolated triangles need refinement, and (ii) locally supported Hermite elements are constructed to achieve the optimal order of approximation.References
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Additional Information
- Charles K. Chui
- Affiliation: Center for Approximation Theory, Texas A&M University, College Station, Texas 77843
- Email: cchui@tamu.edu
- Dong Hong
- Affiliation: Center for Approximation Theory, Texas A&M University, College Station, Texas 77843
- Email: dhong@math.utexas.edu
- Received by editor(s): May 28, 1994
- Received by editor(s) in revised form: December 5, 1994
- Additional Notes: Research supported by NSF Grant No. DMS 92-06928 and ARO Contract DAAH 04-93-G-0047
- © Copyright 1996 American Mathematical Society
- Journal: Math. Comp. 65 (1996), 85-98
- MSC (1991): Primary 41A25, 41A63; Secondary 41A05, 41A15, 65D07
- DOI: https://doi.org/10.1090/S0025-5718-96-00689-8
- MathSciNet review: 1325865