带粘性的Burgers方程的自适应有限元算法

Adaptive Finite Element Method for Burgers Equations with Viscous Term

对于带粘性项的Burgers方程,我们采用特征线有限元方法离散时间导数项和对流项,用分片线性有限元离散空间扩散项,应用Z.Chen[5]关于非线性对流扩散问题的后验误差估计及其估计子。我们采用了CERS加密放粗策略,设计了相应的自适应算法。并在二维情形下进行了数值试验,成功刻画了Burgers方程的击波现象,并且得到了拟最优的收敛阶。

We study the Burgers equations with viscous term.discretized implicitly in time via the method of characteristics and in space via continuous piecewise linear,finite elements.Using the a posteriori error estimate,which was derived by Z.Chen [5] for nonlinear problems,we desined an adaptive algorithm.The CERS strategy was used to refine and coase the meshs in our algorithm.Numerical simulations were implemented in 2D case.Numerical results show that we can capture the shock waves successfully and the quasi-optimal convergence order were also proved numerically.