Two-Grid Partition of Unity Method for Second Order Elliptic Problems
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摘要: 标准的两重网格方法是一种求解二阶椭圆问题的局部并行方法,其计算所得数值解在整个求解区域上并不连续.使用单位分解技术,将各个子区域上的局部解粘合在一起,从而得到全局连续解,并证明此解在H1范数意义下最优.更进一步,可以证明通过在粗网格上修正,能够改善其L2误差.数值例子验证了理论的正确性.Abstract: A two-grid partition of unity method for second order elliptic problems was proposed and analyzed.The standard two-grid method is a local and parallel method which usually leads to a discontinuous solution in the whole computational domain.Partition of unity method was employed to glue all the local solutions together to get global continuous one,which is optimal in H1-norm.Furthermore,it is shown that the L2 error can be improved by using the coarse grid correction.Numerical experiments are reported to support the theory.
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Key words:
- second order elliptic problems /
- two-grid method /
- partition of unity
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