非线性对流扩散方程的双线性元解的高精度分析

Higher accuracy analysis for bilinear finite element solution of nonlinear advection-diffusion equation

利用积分恒等式对发展型非线性对流扩散方程的双线性有限元解进行了高精度分析.给出了L2-模意义下的二阶ε一致收敛结果.进一步,根据Bramble-Hilbert引理推导出了2个高精度的积分恒等式,并由此得到了一个新的渐近展开式.

By using integral identities,the higher accuracy approximation of bilinear conforming finite element for the time-dependent nonlinear advection-diffusion equations is investigated.The optimal ε uniform convergent result is obtained under L2-norm.Based on Bramble-Hilbert lemma,two new integral identities and a asymptotic error expansion are derived.