Superconvergence of Conforming Finite Element for Fourth-Order Singularly Perturbed Problems of Reaction Diffusion Type in 1D
نویسندگان
چکیده
We consider conforming finite element approximation of fourth-order singularly perturbed problems of reaction diffusion type. We prove superconvergence of standard C1 finite element method of degree p on a modified Shishkin mesh. In particular, a superconvergence error bound of ( N−1ln(N + 1))p in a discrete energy norm is established. The error bound is uniformly valid with respect to the singular perturbation parameter . Numerical tests indicate that the error estimate is sharp. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 550–566, 2014
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