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Title: Long-time accurate symmetrized implicit-explicit BDF methods for a class of parabolic equations with non-self-adjoint operators
Authors: Li, B 
Wang, K 
Zhou, Z 
Issue Date: 2020
Source: SIAM journal on numerical analysis, 2020, v. 58, no. 1, p. 189-210
Abstract: An implicit-explicit multistep method based on the backward difference formulae (BDF) is proposed for time discretization of parabolic equations with a non-self-adjoint operator. Implicit and explicit schemes are used for the self-adjoint and anti-self-adjoint parts of the operator, respectively. For a k-step method, some correction terms are added to the starting k-1 steps to maintain kth-order convergence without imposing further compatibility conditions at the initial time. Long-time kth-order convergence for the numerical method is proved under the assumptions that the operator is coercive and that the non-self-adjoint part is low order. Such an operator often appears in practical computation (such as the Stokes-Darcy system) but may violate the standard sectorial angle condition used in the literature for analysis of BDF. In particular, the proposed method and analysis in this paper extend the long-time energy error analysis of the Stokes-Darcy system in Chen et al. [SIAM J. Numer. Anal., 51 (2013), pp. 2563-2584; Numer. Math., 134 (2016), pp. 857-879] to general symmetrized and decoupled BDF methods up to order 6 by using the generating function technique.
Keywords: Backward difference formula
Error estimate
Initial correction
Long-time stability
Non-self-adjiont operator
Parabolic equation
Sectorial angle
Stokes-Darcy system
Publisher: Society for Industrial and Applied Mathematics
Journal: SIAM journal on numerical analysis 
ISSN: 0036-1429
EISSN: 1095-7170
DOI: 10.1137/18M1227536
Rights: © 2020, Society for Industrial and Applied Mathematics.
Unauthorized reproduction of this article is prohibited.
First Published in SIAM Journal on Numerical Analysis in Volume 58, Issue 1, published by the Society for Industrial and Applied Mathematics (SIAM)
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