Finite Element Analysis Of Nonlinear BBM Equation

This paper mainly studies the finite element approximation BBM equation by using the conforming bilinear element and nonconforming EQrot1 element. The new pattern of high accuracy analysis also is made under anisotropic meshes by using of linear triangular element.First of all, the superclose result of finite element solution and the interpolation of the exact solution about H1 norm can be obtained under semi-discrete and four kinds of fully-discrete schemes, with the help of this result, the global superconvergence result can be obtained about H1 norm after applying he interpolation postprocessing technique. The Newton iterative method and the linearized method are used to verify the correctness of theoretical analysis in the numerical experiment part.Then, the superclose result of finite element solution and the interpolation of the exact solution about broken-H1 norm can be obtained under semi-discrete and fullydiscrete schemes by making full use of the two special properties of the EQrot1 element,at the same time, after applying a appropriate interpolation postprocessing operator,the global superconvergence result is acquired. The Newton iterative method and the linearized method are also used to verify the correctness of theoretical analysisFinally, This equation is analyzed under anisotropic meshes by using of the interpolation and projection combination, if only use the projection operator cannot get convergence estimates under anisotropic meshes(previously only in the regular grid with the corresponding results), if only use interpolation operator, utdemands higher smooth and so, the combination of the two under anisotropic meshes can not only reduce the smoothness requirements of utand got the superclose and superconvergence results.