非线性Benjamin-Bona-Mahony方程一个新的低阶混合元方法（英文）

A New Low Order Mixed FEM for Nonlinear Benjamin-Bona-Mahony Equation

基于双线性元和零阶R-T元,建立了非线性Benjamin-Bona-Mahony(BBM)方程的一个新的低阶混合元方法.借助积分恒等式技巧,得到了一个对超逼近分析比较重要的误差估计.对于半离散格式,证明了解的存在性,唯一性和稳定性,然后得到了精确解u在H1模意义下和压力变量p=?u_t在L^2模意义下具有O(h^2)的超逼近和超收敛结果.对于向后欧拉和Crank-Nicolson全离散格式,分别探讨了解的稳定性,且在对时间步长没有任何限制的前提下得到了超逼近结果.

A new low order mixed finite element method（FEM） is proposed for solving nonlinear Benjamin-Bona-Mahony（BBM） equation based on bilinear element and zero order Raviart-Thomas（R-T） element. Applying integral identity technique, an important estimate is proved which is useful for the superclose analysis. For semi-discrete scheme,the existence, uniqueness, stability of the solution are discussed. Then, the superclose properties and global superconvergence results with order O（h2） are deduced for both the exact solution u in H1-norm and the stress variable ？p = ？ut in L2-norm. For backward Euler and Crank-Nicolson fully-discrete schemes, the stability of the solution is discussed and the superclose results are derived without any time-step restriction, respectively.