Matches in SemOpenAlex for { <https://semopenalex.org/work/W2020357712> ?p ?o ?g. }
Showing items 1 to 88 of
88
with 100 items per page.
- W2020357712 endingPage "239" @default.
- W2020357712 startingPage "217" @default.
- W2020357712 abstract "Generalizing the approach of a previous work of the authors, dealing with two-dimensional (2D) problems, we 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 by Axelsson and Vassilevski in the late-1980s, 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. In the present paper new estimates of the constant γ in the strengthened Cauchy–Bunyakowski–Schwarz (CBS) inequality are derived that allow an efficient multilevel extension of the related two-level preconditioners. Representative numerical tests well illustrate the optimal complexity of the resulting iterative solver, also for the case of non-smooth coefficients. The second important achievement concerns the experimental study of AMLI solvers applied to the case of micro finite element (μFEM) simulation. Here the coefficient jumps are resolved on the finest mesh only and therefore the classical CBS inequality based convergence theory is not directly applicable. The obtained results, however, demonstrate the efficiency of the proposed algorithms in this case also, as is illustrated by an example of microstructure analysis of bones." @default.
- W2020357712 created "2016-06-24" @default.
- W2020357712 creator A5048242837 @default.
- W2020357712 creator A5073185577 @default.
- W2020357712 creator A5088656822 @default.
- W2020357712 date "2008-08-01" @default.
- W2020357712 modified "2023-10-18" @default.
- W2020357712 title "Multilevel algorithms for Rannacher–Turek finite element approximation of 3D elliptic problems" @default.
- W2020357712 cites W1485867343 @default.
- W2020357712 cites W1527152660 @default.
- W2020357712 cites W1546004968 @default.
- W2020357712 cites W1668829611 @default.
- W2020357712 cites W1994445516 @default.
- W2020357712 cites W1995096085 @default.
- W2020357712 cites W2002032847 @default.
- W2020357712 cites W2009441498 @default.
- W2020357712 cites W2018685527 @default.
- W2020357712 cites W2051483608 @default.
- W2020357712 cites W2063727723 @default.
- W2020357712 cites W2064625750 @default.
- W2020357712 cites W2065867295 @default.
- W2020357712 cites W2066610136 @default.
- W2020357712 cites W2083054768 @default.
- W2020357712 cites W2090613564 @default.
- W2020357712 cites W2109005370 @default.
- W2020357712 cites W2131738355 @default.
- W2020357712 cites W2147446841 @default.
- W2020357712 cites W2491027544 @default.
- W2020357712 doi "https://doi.org/10.1007/s00607-008-0008-5" @default.
- W2020357712 hasPublicationYear "2008" @default.
- W2020357712 type Work @default.
- W2020357712 sameAs 2020357712 @default.
- W2020357712 citedByCount "7" @default.
- W2020357712 countsByYear W20203577122012 @default.
- W2020357712 countsByYear W20203577122013 @default.
- W2020357712 countsByYear W20203577122014 @default.
- W2020357712 countsByYear W20203577122015 @default.
- W2020357712 crossrefType "journal-article" @default.
- W2020357712 hasAuthorship W2020357712A5048242837 @default.
- W2020357712 hasAuthorship W2020357712A5073185577 @default.
- W2020357712 hasAuthorship W2020357712A5088656822 @default.
- W2020357712 hasBestOaLocation W20203577122 @default.
- W2020357712 hasConcept C11413529 @default.
- W2020357712 hasConcept C121332964 @default.
- W2020357712 hasConcept C126255220 @default.
- W2020357712 hasConcept C134306372 @default.
- W2020357712 hasConcept C135628077 @default.
- W2020357712 hasConcept C208081375 @default.
- W2020357712 hasConcept C2778770139 @default.
- W2020357712 hasConcept C28826006 @default.
- W2020357712 hasConcept C33923547 @default.
- W2020357712 hasConcept C62520636 @default.
- W2020357712 hasConcept C73000952 @default.
- W2020357712 hasConcept C97355855 @default.
- W2020357712 hasConceptScore W2020357712C11413529 @default.
- W2020357712 hasConceptScore W2020357712C121332964 @default.
- W2020357712 hasConceptScore W2020357712C126255220 @default.
- W2020357712 hasConceptScore W2020357712C134306372 @default.
- W2020357712 hasConceptScore W2020357712C135628077 @default.
- W2020357712 hasConceptScore W2020357712C208081375 @default.
- W2020357712 hasConceptScore W2020357712C2778770139 @default.
- W2020357712 hasConceptScore W2020357712C28826006 @default.
- W2020357712 hasConceptScore W2020357712C33923547 @default.
- W2020357712 hasConceptScore W2020357712C62520636 @default.
- W2020357712 hasConceptScore W2020357712C73000952 @default.
- W2020357712 hasConceptScore W2020357712C97355855 @default.
- W2020357712 hasIssue "4" @default.
- W2020357712 hasLocation W20203577121 @default.
- W2020357712 hasLocation W20203577122 @default.
- W2020357712 hasOpenAccess W2020357712 @default.
- W2020357712 hasPrimaryLocation W20203577121 @default.
- W2020357712 hasRelatedWork W2091683908 @default.
- W2020357712 hasRelatedWork W2744240198 @default.
- W2020357712 hasRelatedWork W2952649113 @default.
- W2020357712 hasRelatedWork W2965585506 @default.
- W2020357712 hasRelatedWork W2983613242 @default.
- W2020357712 hasRelatedWork W3202981968 @default.
- W2020357712 hasRelatedWork W4200634329 @default.
- W2020357712 hasRelatedWork W4289097782 @default.
- W2020357712 hasRelatedWork W4301249861 @default.
- W2020357712 hasRelatedWork W75873365 @default.
- W2020357712 hasVolume "82" @default.
- W2020357712 isParatext "false" @default.
- W2020357712 isRetracted "false" @default.
- W2020357712 magId "2020357712" @default.
- W2020357712 workType "article" @default.