Some Estimates With Nonconforming Elements In Domain Decomposition Analysis
Jin-sheng Gu 1, Xian-cheng Hu 21 Department of Mathematics, Capital Normal University, Beijing, China
2 Department of Applied Mathematics, Tsinghua University, Beijing, China
Some essential estimates, especially the so--called extension theorems, are established in this paper, for the nonconforming finite elements with their continuity at the vertices or the edge midpoints of the elements of the quasi--uniform mesh. As in the conforming discrete cases, these estimates play key roles in the theoretical analysis of the nonoverlap domain decomposition methods for the solving of second order self--adjoint elliptic problems discretized by the nonconforming finite element methods.
Key words: Nonconforming finite element; extension theorem; domain decomposition; elliptic problem.