TY - JOUR
T1 - Stability and error estimates for the successive-projection technique with B-splines in time
AU - Ueda, Yuki
AU - Saito, Norikazu
N1 - Funding Information:
The authors thank Professor K. Takizawa (Waseda University) and Professor T.E. Tezduyar (Rice University) who brought the subject to theirattention. The first author was supported by the Program for Leading Graduate Schools, MEXT, Japan . The second author was supported by JST CREST (Japan) Grant Number JPMJCR15D1 , Japan, and JSPS KAKENHI (Japan) Grant Number 15H03635 , Japan.
Funding Information:
The authors thank Professor K. Takizawa (Waseda University) and Professor T.E. Tezduyar (Rice University) who brought the subject to theirattention. The first author was supported by the Program for Leading Graduate Schools, MEXT, Japan. The second author was supported by JST CREST (Japan) Grant Number JPMJCR15D1, Japan, and JSPS KAKENHI (Japan) Grant Number 15H03635, Japan.
Publisher Copyright:
© 2019 Elsevier B.V.
PY - 2019/10/1
Y1 - 2019/10/1
N2 - 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.
AB - 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.
KW - Error estimate
KW - Space–time computation
KW - Stability
UR - http://www.scopus.com/inward/record.url?scp=85063624412&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85063624412&partnerID=8YFLogxK
U2 - 10.1016/j.cam.2019.03.026
DO - 10.1016/j.cam.2019.03.026
M3 - Article
AN - SCOPUS:85063624412
VL - 358
SP - 266
EP - 278
JO - Journal of Computational and Applied Mathematics
JF - Journal of Computational and Applied Mathematics
SN - 0377-0427
ER -