Two-scale composite finite element method for Dirichlet problems on complicated domains |
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Authors: | M Rech S Sauter A Smolianski |
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Institution: | 1. Institut für Mathematik, Universit?t Zürich, Winterthurerch strasse 190, 8057, Zürich, Switzerland
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Abstract: | In this paper, we define a new class of finite elements for the discretization of problems with Dirichlet boundary conditions.
In contrast to standard finite elements, the minimal dimension of the approximation space is independent of the domain geometry
and this is especially advantageous for problems on domains with complicated micro-structures. For the proposed finite element
method we prove the optimal-order approximation (up to logarithmic terms) and convergence estimates valid also in the cases
when the exact solution has a reduced regularity due to re-entering corners of the domain boundary. Numerical experiments
confirm the theoretical results and show the potential of our proposed method. |
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Keywords: | 35J20 65N15 65N30 |
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