Analysis on Superclose Results for Nonlinear BBM Equation with BDF2 Mixed Finite Element Method
A second-order Backward Differential Formula(BDF2)time discretization scheme is constructed for the nonlinear Benjamin-Bona-Mahony(BBM)equation,and a mixed finite element method incorporating bi-linear and zero-order Raviart-Thomas(RT)elements is employed to investigate its superconvergence properties.Firstly,the stability of the approximate equation is established using certain transformation techniques.Second-ly,by utilizing the boundedness of the approximate solution,superclose results are derived.Finally,an example is presented to verify the validity of the theoretical findings.
nonlinear BBM equationBDF2 mixed finite element methodstabilitysuperclose analysis
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