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A C 0 interior penalty method for a singularly‐perturbed fourth‐order elliptic problem on a layer‐adapted mesh
Author(s) -
Franz Sebastian,
Roos HansGörg,
Wachtel Andreas
Publication year - 2014
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.21839
Subject(s) - mathematics , convergence (economics) , polygon mesh , order (exchange) , mathematical analysis , upper and lower bounds , penalty method , geometry , mathematical optimization , finance , economics , economic growth
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