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Original Articles

Convergence and quasi-optimality of an adaptive finite element method for semilinear elliptic problems on L2 errors

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Pages 2337-2354 | Received 15 Jul 2018, Accepted 24 Nov 2019, Published online: 10 Dec 2019
 

Abstract

In this paper, we prove the convergence and quasi-optimality of an adaptive finite element method for semilinear elliptic problems on L2 errors by keeping sufficiently mildly graded meshes. Additional refinements are made to keep the meshes sufficiently mildly graded, but we find that it does not compromise the quasi-optimality of the adaptive finite element method presented in this paper. Numerical examples are provided to illustrate our theoretical results.

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Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work is supported by Nanhu Scholars Program for Young Scholars of XYNU (2016), National Natural Science Foundation of China (11601466), and Doctoral Scientific Research Startup Fund of Xinyang Normal University (15021).

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