Stability and convergence of the variable-step time filtered backward Euler scheme for parabolic equations

Hong lin Liao*, Tao Tang, Tao Zhou

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

1 Citation (Scopus)

Abstract

This work is concerned with numerical analysis of the variable-step time filtered backward Euler scheme (see e.g. DeCaria in SIAM J Sci Comput 43(3):A2130–A2160, 2021) for linear parabolic equations. To this end, we build up a discrete gradient structure of the associated one-leg multi-step scheme of the time filtered backward Euler (FiBE) scheme, and establish the discrete energy dissipation law for the dissipative case. Furthermore, upon developing the discrete energy technique with two new classes of discrete orthogonal convolution kernels, we present the rigorous stability and convergence results for the variable-step FiBE scheme in the L2 norm under a practical step-ratio constraint 1 / 2 ≤ τk/ τk-1≤ 2 for k≥ 2 , where τk is the associated discrete time step. This seems to be the first energy stability and L2 norm error estimate for the variable-step time filtered stiff solver. We also present numerical tests to support the theoretical findings.

Original languageEnglish
Article number39
Number of pages27
JournalBIT Numerical Mathematics
Volume63
Issue number3
Early online date3 Jul 2023
DOIs
Publication statusPublished - Sept 2023

Scopus Subject Areas

  • Software
  • Computer Networks and Communications
  • Computational Mathematics
  • Applied Mathematics

User-Defined Keywords

  • Discrete gradient structure
  • Discrete orthogonal convolution kernels
  • Stability and convergence
  • Time filtered backward Euler

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