对流占优Sobolev方程的最小二乘特征混合有限元方法

A least-squares mixed finite element procedure with the method of characteristics for convection-dominated Sobolev equations

将最小二乘混合有限元法与特征有限元法有效地结合起来处理对流占优Sobolev方程。通过适当选取最小二乘能量泛函,数值方法可以分裂成2个独立的子格式,并且数值方法可以同时逼近解及其梯度,选取较大的时间步长。收敛性分析表明数值方法关于变量u在L2和H1范数意义下均达到最优收敛阶;关于变量σ在H(div;Ω)范数意义下达到最优收敛阶。

A least-squares mixed finite element procedure with the method of characteristics for convection-dominated Sobolev equations was presented. By properly selecting the least-squares functional, the procedure can be split into two independent subprocedures. The solution u and the flux σ can be obtained directly. Moreover, this method permits the use of large steps. The convergence analysis shows that the method yields the approximate solutions with optimal accuracy in L^2 （Ω ） and H^1 （ Ω） norms for u and H（div;Ω）norm for the flux σ.