High accuracy analysis of the lowest order H 1-Galerkin mixed finite element method for nonlinear sine-Gordon equations

作者：Shi, Dong-yang; Wang, Fen-ling^*; Zhao, Yan-min^*

来源：Acta Mathematicae Applicatae Sinica-English Series, 2017, 33(3): 699-708.

DOI：10.1007/s10255-017-0692-z

• nonlinear sine-Gordon equations
• H1-Galerkin MFEM
• superclose estimates
• semi-discrete and fully-discrete schemes

The lowest order H (1)-Galerkin mixed finite element method (for short MFEM) is proposed for a class of nonlinear sine-Gordon equations with the simplest bilinear rectangular element and zero order Raviart-Thomas element. Base on the interpolation operator instead of the traditional Ritz projection operator which is an indispensable tool in the traditional FEM analysis, together with mean-value technique and high accuracy analysis, the superclose properties of order O(h (2))/O(h (2) + tau (2)) in H (1)-norm and H(div;Omega)-norm are deduced for the semi-discrete and the fully-discrete schemes, where h, tau denote the mesh size and the time step, respectively, which improve the results in the previous literature.

• 出版日期2017-7
• 单位郑州大学; 许昌学院