对流扩散方程的一种基于界面罚条件的非重叠区域分解法

On Non-overlapping Domain Decomposition Method of Convection-diffusion Equations Based on Interface Penalty Term

应用基于界面罚条件的非重叠区域分解法求解稳态对流占优的对流扩散方程,分析了该方法的相容性,并对其有限元解进行了误差估计,证明当将罚参数ε选取得足够小时,用k阶有限元空间来逼近弱解空间,能得到最优阶的误差估计。

We applied a non-overlapping domain decomposition method via a penalization on the interface to convection-dominated convection-diffusion equations and analyzed its consistency. And the finding is that the error estimates are optimal when used finite elements of degree k and set the parameter ε small enough.