TY - JOUR
T1 - Second Order Unconditionally Stable and Convergent Linearized Scheme for a Fluid-Fluid Interaction Model
AU - Li , Wei
AU - Huang , Pengzhan
AU - He , Yinnian
JO - Journal of Computational Mathematics
VL - 1
SP - 72
EP - 93
PY - 2022
DA - 2022/11
SN - 41
DO - http://doi.org/10.4208/jcm.2104-m2020-0265
UR - https://global-sci.org/intro/article_detail/jcm/21170.html
KW - Fluid-fluid interaction model, Unconditional stability, Second order temporal accuracy, Error estimate.
AB - <p style="text-align: justify;">In this paper, a fully discrete finite element scheme with second-order temporal accuracy is proposed for a fluid-fluid interaction model, which consists of two Navier-Stokes equations coupled by a linear interface condition. The proposed fully discrete scheme is a combination of a mixed finite element approximation for spatial discretization, the second-order backward differentiation formula for temporal discretization, the second-order Gear&#39;s extrapolation approach for the interface terms and extrapolated treatments in linearization for the nonlinear terms. Moreover, the unconditional stability is established by rigorous analysis and error estimate for the fully discrete scheme is also derived. Finally, some numerical experiments are carried out to verify the theoretical results and illustrate the accuracy and efficiency of the proposed scheme.</p>