Abstract
We study the successive projection technique with B-splines proposed by Takizawa and Tezduyar in 2014 (Computational Mechanics, vol. 53). The projection is considered for X-valued functions with a Banach space X. Stability and error estimates in the L ∞ (0,T;X) norm are studied for B-spline basis functions of degree p=1,2,3,4. The quasi-uniformity of partition is always assumed and the projection is stable if p=1. We prove that, for p=2,3,4, the uniformity of partition is a sufficient condition for stability to hold. Furthermore, we infer from numerical experiments that stability holds at least for p=5,6,7. We also prove the error estimate using the spline-preserving property of the projector if the projection is stable.
Original language | English |
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Pages (from-to) | 266-278 |
Number of pages | 13 |
Journal | Journal of Computational and Applied Mathematics |
Volume | 358 |
DOIs | |
Publication status | Published - 2019 Oct 1 |
Externally published | Yes |
Keywords
- Error estimate
- Space–time computation
- Stability
ASJC Scopus subject areas
- Computational Mathematics
- Applied Mathematics