非线性对流扩散方程迎风有限元的自适应方法

Adaptive Upwind FEM for Nonlinear Convection-diffusion Equations

对二维非线性发展型对流扩散方程的迎风有限元格式给出了显式后验误差估计,建立了真实误差由后验误差估计器上下界定的估计式,由此给出了相应的自适应算法,数值试验表明了该算法的有效性.

The explicit a posterior error estimators for the upwind finite element scheme of two dimensional nonlinear convection-diffusion equations is given, and the fact that the true error is bounded by these a posterior error estimators is proved. Then an adaptive method based on these estimators is designed. And the numerical results show that this method is feasible.