A class of nonconforming finite elements is considered in this paper, which is continuous only at the nodes of the quasi-uniform mesh. We show that there exists an essential estimate which indicates the equivalence re...A class of nonconforming finite elements is considered in this paper, which is continuous only at the nodes of the quasi-uniform mesh. We show that there exists an essential estimate which indicates the equivalence relation, independent of the mesh parameter, between the energies of the nonconforming discrete harmonic extensions in different subdomains. The essential estimate is of great importance in the analysis of the nonoverlapping domain decomposition methods applied to second order partial differential equations discretized by nonconforming finite elements.展开更多
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 o...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.展开更多
基金The Project Supported by National Natural Science Foundation of China.
文摘A class of nonconforming finite elements is considered in this paper, which is continuous only at the nodes of the quasi-uniform mesh. We show that there exists an essential estimate which indicates the equivalence relation, independent of the mesh parameter, between the energies of the nonconforming discrete harmonic extensions in different subdomains. The essential estimate is of great importance in the analysis of the nonoverlapping domain decomposition methods applied to second order partial differential equations discretized by nonconforming finite elements.
文摘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.
