Record link: 
http://hdl.handle.net/20.500.12708/155478
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Title: 
A new proof for existence of H-matrix approximants to the inverse of FEM matrices: the Dirichlet problem for the Laplacian
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Citation: 
Faustmann, M., Melenk, J. M., & Praetorius, D. (2014). A new proof for existence of H-matrix approximants to the inverse of FEM matrices: the Dirichlet problem for the Laplacian. In Spectral and High Order Methods for Partial Differential Equations - ICOSAHOM 2012 (pp. 249–259). Springer. https://doi.org/10.1007/978-3-319-01601-6_20
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Publisher DOI: 
10.1007/978-3-319-01601-6_20
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Publication Type: 
Inproceedings - Full-Paper Contribution
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Language: 
English
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Authors: 
Faustmann, Markus 
Melenk, Jens M. 
Praetorius, Dirk 
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Organisational Unit: 
E101-02 - Forschungsbereich Numerik 
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Published in: 
Spectral and High Order Methods for Partial Differential Equations - ICOSAHOM 2012 
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ISBN: 
978-3-319-01601-6
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Volume: 
95
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DOI of the book: 
10.1007/978-3-319-01601-6
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Date (published): 
1-Jan-2014
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Event name: 
International Conference on Spectral and High Order Methods (ICOSAHOM 2012) 
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Event date: 
25-Jun-2012 - 29-Jun-2012
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Event place: 
Gammarth, Tunisia
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Number of Pages: 
11
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Publisher: 
Springer
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Abstract: 
We study the question of approximability of the inverse of the FEM stiffness matrix for the Laplace problem with Dirichlet boundary conditions by blockwise low rank matrices such as those given by the H-matrix format introduced in [Hac99]. We show that exponential convergence in the local block rank r can be achieved. Unlike prior works [BH03, B¨or10a], our analysis avoids any a priori coupling r = O(| log h|) of r and the mesh width h. Moreover, the techniques developed can be used to analyze other boundary conditions as well.
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Research Areas: 
Mathematical and Algorithmic Foundations: 100%
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Science Branch: 
Mathematik
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Appears in Collections:
Conference Paper

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