Stability and error estimates for the successive-projection technique with B-splines in time

Yuki Ueda, Norikazu Saito

Research output: Contribution to journalArticle

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 languageEnglish
Pages (from-to)266-278
Number of pages13
JournalJournal of Computational and Applied Mathematics
Volume358
DOIs
Publication statusPublished - 2019 Oct 1
Externally publishedYes

Keywords

  • Error estimate
  • Space–time computation
  • Stability

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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