Application of Hierarchical Decomposition: Preconditioners and Error Estimates for Conforming and Nonconforming FEM

A successive refinement of a finite element grid provides a sequence of nested grids and hierarchy of nested finite element spaces as well as a natural hierarchical decomposition of these spaces. In the case of numerical solution of elliptic boundary value problems by the conforming FEM, this sequence can be used for building both multilevel preconditioners and error estimates. For a nonconforming FEM, multilevel preconditioners and error estimates can be introduced by means of a hierarchy, which is constructed algebraically starting from the finest discretization.

• Type: Conference
• Year: 2007
• Where: LSSC
• Authors: Radim Blaheta
• Keywords: Applied Computing, Error Estimates, LSSC 2007, Multilevel Preconditioners, finite Element