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A constructive a priori error estimation for finite element discretizations in a non-convex domain using singular functions

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概要 In solving elliptic problems by the finite element method in a bounded domain with has a re-entrant corner, the rate of convergence could be improved by adding a singular function to the usual $ C^0 $... approximating basis. When the domain is enclosed by line segments which forms a corner of $ pi/2 $ or $ 3pi/2 $, we have obtained an explicit an a priori $ H^1 $ error estimation of $ O(h) $ for such a finite element solution of the Poisson equation. Particularly, we emphasize that all constants in our error estimates are numerically determined, which plays an essential role in the numerical verification of solutions for non-linear elliptic problems.続きを見る

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登録日 2009.04.22
更新日 2018.02.28