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High order local approximations to derivatives in the finite element method


Author: Vidar Thomée
Journal: Math. Comp. 31 (1977), 652-660
MSC: Primary 65D25; Secondary 65L10
MathSciNet review: 0438664
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Abstract: Consider the approximation of the solution u of an elliptic boundary value problem by means of a finite element Galerkin method of order r, so that the approximate solution $ {u_h}$ satisfies $ {u_h} - u = O({h^r})$. Bramble and Schatz (Math. Comp., v. 31, 1977, pp. 94-111) have constructed, for elements satisfying certain uniformity conditions, a simple function $ {K_h}$ such that $ {K_h}\; \ast \;{u_h} - u = O({h^{2r - 2}})$ in the interior. Their result is generalized here to obtain similar superconvergent order interior approximations also for derivatives of u.


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DOI: http://dx.doi.org/10.1090/S0025-5718-1977-0438664-4
Article copyright: © Copyright 1977 American Mathematical Society