非线性色散耗散波动方程混合元方法的超逼近分析

Superclose Analysis of a Mixed Finite Element Method for Nonlinear Dispersion-Dissipative Wave Equation

主要基于不完全双二次元和一阶BDFM元对非线性色散耗散波动方程建立了一种混合元格式.首先在半离散格式下,利用单元具有的高精度结果和插值与投影相结合的技巧,得到了原始变量和中间变量的超逼近结果.然后在时间方向上借助一个新的二阶差分格式,建立了该方程的全离散逼近格式,并进一步给出了原始变量和中间变量的高精度分析.

A mixed finite element method is established for nonlinear dispersion dissipative wave equation based on incomplete biquadratic element and one order BDFM element.Firstly,applying properties of the elements and the technique of combining interpolation and projection,the superclose results for the primitive variable and the intermediate variable are deduced in the semi-discrete scheme.Then through a new second difference scheme in time direction,a fully-discrete scheme is constructed and the high accuracy analysis is given for the primitive variable and the intermediate variable.