广义Stokes问题的区域分裂解法及其事后误差估算

本文的主要目的在于将Ｌａｇｒａｎｇｅ乘子技术应用于广义Ｓｔｏｋｅｓ问题的非匹配网格上的区域分裂解法中；这种方法非常适用于有限元空间近似。Ｌａｇｒａｎｇｅ乘子是在分段常数函数的空间中近似的。同时，基于求解当地问题，我们还构造了离散近似的事后误差估算器，并基于此对网格进行了自适应处理。数值实验的结果验证了本文所发展的方法。

Domain Decomposition for Generalized Stokes Problem and A Posterior Error Estimation

The main goal of this article is the application of Lagrange multiplier to domain decomposition for generalized Stokes problem; This method is very suitable to the finite element space approximation. Lagrange multiplier is approximated in the space of piecewise constant functions. We also construct the a posteriori error estimators based on solving local problems and refine adaptively meshes using the error estimators as criteria. The results of numerical experiments validate the method developed in this work.