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http://dx.doi.org/10.11568/kjm.2018.26.3.467

POSTPROCESSING FOR THE RAVIART-THOMAS MIXED FINITE ELEMENT APPROXIMATION OF THE EIGENVALUE PROBLEM  

Kim, Kwang-Yeon (Department of Mathematics Kangwon National University)
Publication Information
Korean Journal of Mathematics / v.26, no.3, 2018 , pp. 467-481 More about this Journal
Abstract
In this paper we present a postprocessing scheme for the Raviart-Thomas mixed finite element approximation of the second order elliptic eigenvalue problem. This scheme is carried out by solving a primal source problem on a higher order space, and thereby can improve the convergence rate of the eigenfunction and eigenvalue approximations. It is also used to compute a posteriori error estimates which are asymptotically exact for the $L^2$ errors of the eigenfunctions. Some numerical results are provided to confirm the theoretical results.
Keywords
eigenvalue problem; mixed finite element method; super-convergence; postprocessing; asymptotic exactness;
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