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Superconvergence of conforming finite element for fourth‐order singularly perturbed problems of reaction diffusion type in 1D
Author(s) -
Guo Hailong,
Huang Can,
Zhang Zhimin
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.21827
Subject(s) - superconvergence , mathematics , singular perturbation , finite element method , norm (philosophy) , reaction–diffusion system , perturbation (astronomy) , mathematical analysis , type (biology) , upper and lower bounds , partial differential equation , physics , political science , law , thermodynamics , ecology , quantum mechanics , biology
We consider conforming finite element approximation of fourth‐order singularly perturbed problems of reaction diffusion type. We prove superconvergence of standard C 1 finite element method of degree p on a modified Shishkin mesh. In particular, a superconvergence error bound of( N − 1 ln ( N + 1 ) ) pin a discrete energy norm is established. The error bound is uniformly valid with respect to the singular perturbation parameter ϵ. Numerical tests indicate that the error estimate is sharp. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 550–566, 2014