M. Faustmann, J. Melenk, D. Praetorius:

"H-matrix approximability of the inverses of FEM matrices";

in: "ASC Report 20/2013", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2013, ISBN: 978-3-902627-06-3, 1 - 23.

We study the question of approximability for the inverse of the FEMstiffness matrix for (scalar) second order elliptic boundary value problems 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. We also show that exponentially accurate LU-decompositions in the

H-matrix format are possible for the stiffness matrices arising in the FEM. Unlike prior works, our analysis avoids any coupling of the block rank r and the mesh width h and also covers mixed

Dirichlet-Neumann-Robin boundary conditions.

http://www.asc.tuwien.ac.at/preprint/2013/asc20x2013.pdf

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