Two-level algorithms for Rannacher-Turek FEM

• Date: 2006
• Main Authors: Georgiev, I., Kraus, J., Margenov, S.
• Format: Article
• Language: English
• Published: Інститут програмних систем НАН України 2006
• Subjects: Прикладне програмне забезпечення
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/1583
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Two-level algorithms for Rannacher-Turek FEM / I. Georgiev, J. Kraus, S.Margenov // Проблеми програмування. — 2006. — N 2-3. — С. 694-700. — Бібліогр.: 6 назв. — англ.

In this paper a multiplicative two-level preconditioning algorithm for second order elliptic boundary value problems is
 considered, where the discretization is done using Rannacher-Turek non-conforming rotated bilinear finite elements on
 quadrilaterals. An important point to make is that in this case 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 originally introduced for conforming finite elements. The proposed
 variant of hierarchical two-level splitting is first defined in a rather general setting. Then, the involved parameters are studied and
 optimized. The major contribution of the paper is the derived uniform estimates of the constant in the strengthened CBS
 inequality which allow the efficient multilevel extension of the related two-level preconditioners.