The construction of preconditioners for elliptic problems by substructuring. I
Mathematics of Computation
Efficient preconditioning for the p-version finite element method in two dimensions
SIAM Journal on Numerical Analysis
SIAM Journal on Numerical Analysis
Journal of Computational and Applied Mathematics
Multigrid Solver for the Inner Problem in Domain Decomposition Methods for p-FEM
SIAM Journal on Numerical Analysis
Multiresolution weighted norm equivalences and applications
Numerische Mathematik
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In this paper, a uniformly elliptic second order boundary value problem in 2D is discretized by the p-version of the finite element method. An inexact Dirichlet-Dirichlet domain decomposition preconditioner for the system of linear algebraic equations is investigated. The ingredients of such a preconditioner are a preconditioner for the Schur complement, a preconditioner for the subdomains and an extension operator operating from the edges of the elements into their interior. Using methods of multi-resolution analysis, we propose a new method in order to compute the extension efficiently. Numerical experiments show the optimal performance of the described extension.