TY - JOUR
T1 - Stability and convergence of the variable-step time filtered backward Euler scheme for parabolic equations
AU - Liao, Hong lin
AU - Tang, Tao
AU - Zhou, Tao
N1 - This work is supported by NSF of China under Grant Numbers 12071216, 11731006, 12288201 and NNW2018-ZT4A06 project.
Publisher Copyright:
© 2023, The Author(s), under exclusive licence to Springer Nature B.V.
PY - 2023/9
Y1 - 2023/9
N2 - 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.
AB - 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.
KW - Discrete gradient structure
KW - Discrete orthogonal convolution kernels
KW - Stability and convergence
KW - Time filtered backward Euler
UR - http://www.scopus.com/inward/record.url?scp=85163861474&partnerID=8YFLogxK
U2 - 10.1007/s10543-023-00982-y
DO - 10.1007/s10543-023-00982-y
M3 - Journal article
AN - SCOPUS:85163861474
SN - 0006-3835
VL - 63
JO - BIT Numerical Mathematics
JF - BIT Numerical Mathematics
IS - 3
M1 - 39
ER -