Design of Adaptive Finite Element Software - The Finite Element Toolbox ALBERTA

By Alfred Schmidt, Kunibert G. Siebert. Lecture Notes in Computational Science and Engineering, 2005

364 citations recorded by the source corpus.

Subfields: Computational Mechanics, Information Systems, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/6d95f85536e865881644add39b9700179c344f19

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In Computational Mechanics

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Citations in the corpus

An h-narrow band finite-element method for elliptic equations on implicit surfaces (2010, methodology): “The Finite Element Toolbox ALBERTA.”
Adaptive reduced basis finite element heterogeneous multiscale method (2013, background): “Several marking strategies have been proposed in the literature, for example, [36, 37, 16].”
Quasioptimal cardinality of AFEM driven by nonresidual estimators (2012, methodology): “…finite overlapping, but the number of them is equivalent to the cardinality ofT, that is #KT ≈ #T (3.1) In contrast to Cascónet al. (2008), to develop our theory we will now need to consider several levels of refinement (or subdivision depth) between two (not necessarily consecutive) meshesT 6 T∗.”
Finite element methods for surface PDEs* (2013, methodology): “Schnakenberg (1979), ‘Simple chemical reaction systems with limit cycle behaviour’, J.”
A generic grid interface for parallel and adaptive scientific computing. Part II: implementation and tests in DUNE (2008, methodology): “AlbertaGrid: The grid manager of the ALBERTA toolbox [18].”
Theory of adaptive finite element methods: An introduction (2009, methodology): “Procedure MARK takes the usual value of θest = 0.5 [32, 52, 53, 63 ], and procedure REFINE subdivides all elements in Mk by using two bisections.”
Quasi-Optimal Convergence Rate for an Adaptive Finite Element Method (2008, neutral): “5 [8, 17, 18, 21], and procedure REFINE subdivides all elements in Mk by using two bisections.”
Adaptive isogeometric analysis by local h-refinement with T-splines (2010, background): “However, though being well understood and available in various academic codes [2,18], adaptive methods with a posteriori error control have so far not become widespread in commercial software.”