TY - JOUR
T1 - Stability and error estimates for the successive-projection technique with B-splines in time
AU - Ueda, Yuki
AU - Saito, Norikazu
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 -