Regularity and a priori error analysis of a Ventcel problem in polyhedral domains |
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Authors: | Serge Nicaise Hengguang Li Anna Mazzucato |
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Institution: | 1. LAMAV, FR CNRS 2956, Institut des Sciences et Techniques of Valenciennes, Université de Valenciennes et du Hainaut Cambrésis, Valenciennes, Cedex 9, France;2. Department of Mathematics, Wayne State University, Detroit, MI, USA;3. Penn State University, University Park, PA, USA |
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Abstract: | We consider the regularity of a mixed boundary value problem for the Laplace operator on a polyhedral domain, where Ventcel boundary conditions are imposed on one face of the polyhedron and Dirichlet boundary conditions are imposed on the complement of that face in the boundary. We establish improved regularity estimates for the trace of the variational solution on the Ventcel face and use them to derive a decomposition of the solution into a regular and a singular part that belongs to suitable weighted Sobolev spaces. This decomposition, in turn, via interpolation estimates both in the interior as well as on the Ventcel face, allows us to perform an a priori error analysis for the finite element approximation of the solution on anisotropic graded meshes. Numerical tests support the theoretical analysis. Copyright © 2016 John Wiley & Sons, Ltd. |
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Keywords: | elliptic boundary value problems Ventcel boundary conditions polyhedral domains weighted Sobolev spaces finite element anistropic meshes |
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