对流扩散方程的三次有限体积元法

Cubic Finite Volume Element Method for Convective Diffusion Equations

针对对流扩散方程,用最佳应力节点构建对偶网格剖分,并基于分片三次Lagrange插值试探函数空间和分片常数检验函数空间,构造了Crank-Nicolson三次有限体积元格式并证明了L2范数误差估计。进一步,在时间上采用Richardson外推法,构造了时间与空间均有四阶精度的格式,并给出数值算例验证了理论分析结果以及所提格式的有效性。

The optimal stress points is used to construct the dual partition,and based on the trial function space of piecewise cubic Lagrange interpolation and the test function space of piecewise constant,the Crank-Nicolson cubic finite volume element scheme is constructed for the convective diffusion equation.The error estimation of L2-norm is proved.Furthermore,by using the Richardson’s extrapolation method in time,a scheme with fourth-order precision in both time and space is constructed.Numerical examples are given to verify the theoretical analysis results and the validity of the proposed scheme.