TY - JOUR
T1 - Second-Order Convergence of the Linearly Extrapolated Crank–Nicolson Method for the Navier–Stokes Equations with H1 Initial Data
AU - Li, Buyang
AU - Ma, Shu
AU - Wang, Na
N1 - Funding Information:
The research of Buyang Li and Shu Ma were partially funded by the internal grant ZZKQ at The Hong Kong Polytechnic University. The research of Na Wang was partially funded by the National Natural Science Foundation of China (NSFC Grant U1930402).
Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.
PY - 2021/9
Y1 - 2021/9
N2 - This article concerns the numerical approximation of the two-dimensional nonstationary Navier–Stokes equations with H1 initial data. By utilizing special locally refined temporal stepsizes, we prove that the linearly extrapolated Crank–Nicolson scheme, with the usual stabilized Taylor–Hood finite element method in space, can achieve second-order convergence in time and space. Numerical examples are provided to support the theoretical analysis.
AB - This article concerns the numerical approximation of the two-dimensional nonstationary Navier–Stokes equations with H1 initial data. By utilizing special locally refined temporal stepsizes, we prove that the linearly extrapolated Crank–Nicolson scheme, with the usual stabilized Taylor–Hood finite element method in space, can achieve second-order convergence in time and space. Numerical examples are provided to support the theoretical analysis.
KW - Error estimate
KW - Linearly extrapolated Crank–Nicolson method
KW - Locally refined stepsizes
KW - Navier–Stokes equations
KW - Nonsmooth initial data
UR - http://www.scopus.com/inward/record.url?scp=85111707569&partnerID=8YFLogxK
U2 - 10.1007/s10915-021-01588-8
DO - 10.1007/s10915-021-01588-8
M3 - Journal article
AN - SCOPUS:85111707569
VL - 88
SP - 1
EP - 20
JO - Journal of Scientific Computing
JF - Journal of Scientific Computing
SN - 0885-7474
IS - 3
M1 - 70
ER -