Superconvergence of a finite element method for linear integro-differential problems

Do Y. Kwak, Sungyun Lee and Qian Li

International Journal of Mathematics and Mathematical Sciences, 2000, vol. 23, 1-17

Abstract:

We introduce a new way of approximating initial condition to the semidiscrete finite element method for integro-differential equations using any degree of elements. We obtain several superconvergence results for the error between the approximate solution and the Ritz-Volterra projection of the exact solution. For k > 1 , we obtain first order gain in L p ( 2 ≤ p ≤ ∞ ) norm, second order in W 1 , p ( 2 ≤ p ≤ ∞ ) norm and almost second order in W 1 , ∞ norm. For k = 1 , we obtain first order gain in W 1 , p ( 2 ≤ p ≤ ∞ ) norms. Further, applying interpolated postprocessing technique to the approximate solution, we get one order global superconvergence between the exact solution and the interpolation of the approximate solution in the L p and W 1 , p ( 2 ≤ p ≤ ∞ ) .

Date: 2000
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:412102

DOI: 10.1155/S0161171200001940

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