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 cond...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 secondorder backward differentiation formula for temporal discretization,the second-order Gear’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.展开更多
基金supported by the Natural Science Foundation of China(grant numbers 11861067 and 11771348)Natural Science Foundation of Xinjiang Province(grant number 2021D01E11).
文摘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 secondorder backward differentiation formula for temporal discretization,the second-order Gear’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.
