非线性对流扩散方程非协调EQ_1^(rot)元解的一致收敛性分析

Uniform convergence analysis for EQ_1^(rot) nonconforming finite element approximation to nonlinear advection-diffusion equations

讨论了非定常非线性对流扩散方程的EQ_1^(rot)非协调元的逼近问题.通过利用积分恒等式和平均值技巧,并借助于EQ_1^(rot)元所具备的的两个特殊性质:(a)当精确解属于H^3(Ω)时,其相容误差为O(h^2)阶,比它的插值误差高一阶;(b)插值算子与Ritz投影算子等价,得出了关于方程中所出现的扩散参数ε的最优一致误差估计.

In this paper, the EQ1^rot nonconforming finite element approximation to the nonlinear advection-diffusion equations with unsteady coefficients is discussed. By use of integral identities and mean-value techniques, and the following two special properties of this element： （a） the consistency error is of order O（h^2）, an order higher than its interpolation error O（h）, when the exact solution belongs to H3（Ω）; and （b） the interpolation operator is equivalent to its Ritz projection operator, the uniform optimal error estimate is obtained with respect to the diffusion parameter appeared in the equation considered.