Multilevel algorithms for Rannacher-Turek finite element approximation of 3D elliptic problems

Generalizing the approach of a previous work [15] the authors present multilevel preconditioners for three-dimensional (3D) elliptic problems discretized by a family of Rannacher Turek non-conforming finite elements. Preconditioners based on various multilevel extensions of two-level finite element methods (FEM) lead to iterative methods which often have an optimal order computational complexity with respect to the number of degrees of freedom of the system. Such methods were first presented in [6, 7], and are based on (recursive) two-level splittings of the finite element space. An important point to make is that in the case of non-conforming elements the finite element spaces corresponding to two successive levels of mesh refinement are not nested in general. To handle this, a proper two-level basis is required to enable us to fit the general framework for the construction of two-level preconditioners for conforming finite elements and to generalize the method to the multilevel case...

• Type: Journal
• Year: 2008
• Where: COMPUTING
• Authors: Ivan Georgiev, Johannes Kraus, Svetozar Margenov
• Keywords: COMPUTING 2008, Finite Elements, Multilevel, Multilevel Extension