Nonlinear Theory and Its Applications, IEICE
Online ISSN : 2185-4106
Special section on Recent Progress in Verified Numerical Computations
Remarks on computable a priori error estimates for finite element solutions of elliptic problems
Akitoshi TakayasuXuefeng LiuShin'ichi Oishi
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Volume 5 (2014) Issue 1 Pages 53-63

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Abstract

For Poisson's equation over a polygonal domain of general shape, the solution of which may have a singularity around re-entrant corners, we provide an explicit a priori error estimate for the approximate solution obtained by finite element methods of high degree. The method used herein is a direct extension of the one developed in preceding paper of the second and third listed authors, which provided a new approach to deal with the singularity by using linear finite elements. In the present paper, we also give a detailed discussion of the dependency of the convergence order on solution singularities, mesh sizes and degrees of the finite element method used.

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© 2014 The Institute of Electronics, Information and Communication Engineers
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