TY - JOUR
T1 - On the convergence of Variational multiscale methods based on Newton's iteration for the incompressible flows
AU - Shi, Feng
AU - Zheng, Haibiao
AU - Yu, Jiaping
AU - Li, Ying
N1 - Publisher Copyright:
© 2014 Elsevier Inc.
PY - 2014/12/1
Y1 - 2014/12/1
N2 - In this paper, the convergence of a general algorithm with θ-type stabilization form for the variational multiscale (VMS) method is presented. Meanwhile, explicit-type and implicit-type algorithms with linear convergence and quadratic convergence are derived from the θ-type algorithm, respectively. The combination of explicit-type and implicit-type algorithms are applied to adaptive VMS, which shows good efficiency. Finally, some numerical tests are shown to support the convergence analysis.
AB - In this paper, the convergence of a general algorithm with θ-type stabilization form for the variational multiscale (VMS) method is presented. Meanwhile, explicit-type and implicit-type algorithms with linear convergence and quadratic convergence are derived from the θ-type algorithm, respectively. The combination of explicit-type and implicit-type algorithms are applied to adaptive VMS, which shows good efficiency. Finally, some numerical tests are shown to support the convergence analysis.
KW - Linear convergence
KW - Navier-Stokes equations
KW - Newton's iteration
KW - Quadratic convergence
KW - Variational multiscale method
UR - https://www.scopus.com/pages/publications/84921999758
U2 - 10.1016/j.apm.2014.04.049
DO - 10.1016/j.apm.2014.04.049
M3 - 文章
AN - SCOPUS:84921999758
SN - 0307-904X
VL - 38
SP - 5726
EP - 5742
JO - Applied Mathematical Modelling
JF - Applied Mathematical Modelling
IS - 23
ER -