论文摘要
本文主要讨论了下面的两个问题。 在第一章中我们展现了一种Mortar类型的旋转Q1有限元的多重网格方法。为了构造和分析这种方法,我们定义了一些算子,在这些算子的基础上定义并且证明了这种V循环的多重网格是一致收敛的,它的收敛率不依赖于网格的尺寸和层数。我们通过数值实验验证了理论分析的正确性。 我们在第二章中构造了求解用旋转Q1有限元离散椭圆型偏微分方程的区域分解方法。因为旋转Q1有限元空间不包含任何协调的有限元子空间,所以我们使用了特殊的粗网格空间。我们证明预优问题的条件数是最优的。
论文目录
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