A C0 interior penalty method for a singularly‐perturbed fourth‐order elliptic problem on a layer‐adapted mesh |
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Authors: | Sebastian Franz Hans‐Görg Roos Andreas Wachtel |
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Affiliation: | 1. Institut für Numerische Mathematik, Technische Universit?t Dresden, , 01062 Dresden, Germany;2. Department of Mathematics and Statistics, University of Strathclyde, , Glasgow G1 1XH, Scotland |
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Abstract: | We analyze the convergence of a continuous interior penalty (CIP) method for a singularly perturbed fourth‐order elliptic problem on a layer‐adapted mesh. On this anisotropic mesh, we prove under reasonable assumptions uniform convergence of almost order k ? 1 for finite elements of degree k ≥ 2. This result is of better order than the known robust result on standard meshes. A by‐product of our analysis is an analytic lower bound for the penalty of the symmetric CIP method. Finally, our convergence result is verified numerically. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 838–861, 2014 |
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Keywords: | anisotropic meshes interior penalties singular perturbation stabilisation |
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