Abstract
In the present paper we concentrate on algebraic two-level and multilevel preconditioners for symmetric positive definite problems arising from discretization by 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 in order to fit the general framework for the construction of two-level preconditioners for conforming finite elements and to generalize the methods to the multilevel case.
The proposed variants of hierarchical two-level basis are first introduced in a rather general setting. Then, the involved parameters are studied and optimized. As will be shown, the obtained bounds – in particular – give rise to optimal order AMLI methods of additive type. The presented numerical tests fully confirm the theoretical estimates.
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Georgiev, I., Kraus, J., Margenov, S. (2007). Multilevel Preconditioning of 2D Rannacher-Turek FE Problems; Additive and Multiplicative Methods. In: Boyanov, T., Dimova, S., Georgiev, K., Nikolov, G. (eds) Numerical Methods and Applications. NMA 2006. Lecture Notes in Computer Science, vol 4310. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70942-8_6
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DOI: https://doi.org/10.1007/978-3-540-70942-8_6
Publisher Name: Springer, Berlin, Heidelberg
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