Abstract
From the very efficient use of hierarchical techniques for the quick solution of finite element equations in case of linear elements, we discuss the generalization of these preconditioners to higher order elements and to the problem of crack growth, where the introduction to of the crack opening would destroy existing mesh hierarchies. In the first part of this paper, we deal with the higher order elements. Here, especially elements based on cubic polynomials require more complicate tasks such as the definition of ficticious spaces and the Ficticious Space Lemma. A numerical example demonstrates that iteration numbers similar to the linear case are obtained.
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Meyer, A. (2006). Efficient Preconditioners for Special Situations in Finite Element Computations. In: Hoffmann, K.H., Meyer, A. (eds) Parallel Algorithms and Cluster Computing. Lecture Notes in Computational Science and Engineering, vol 52. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-33541-2_5
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DOI: https://doi.org/10.1007/3-540-33541-2_5
Publisher Name: Springer, Berlin, Heidelberg
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