非线性对流扩散问题的动态网格特征混合元方法

A characteristic mixed method with dynamic finite-element space for nonlinear convection-dominated diffusion problems

将特征混合有限元方法与动态网格相结合来处理非线性对流扩散问题 .在不同时间层采用不同的有限元空间 ,并且将近似解在加权L2 范数下投影到下一个有限元空间作为下一个时间层的初始值 .

A method using a combination of the characteristic mixed method with dynamic finite element space is formulated to solve nonlinear convection dominated diffusion problem. Different number elements and different basis functions are adoped at different time levels; and the approximate solution is rejected onto the next finite element space in weighted L 2 norm for starting a new time step. Error estimates show that the method has optimal covergent rate in some sense.