A posteriori error estimates for a modified Morley FEM
A.K. Dond, D. Gallistl, S. Nayak, M. Schedensack
TL;DR
This paper develops reliable and efficient residual-based a posteriori error estimators for a modified Morley finite element method applied to singularly perturbed biharmonic and nonlinear von Kármán equations, with adaptive algorithms tested numerically.
Contribution
It introduces new a posteriori error estimators for the modified Morley FEM and demonstrates their effectiveness for complex PDEs.
Findings
Error estimators are proven reliable and efficient.
Adaptive algorithm improves solution accuracy.
Numerical experiments confirm theoretical results.
Abstract
Residual-based a~posteriori error estimators are derived for the modified Morley FEM, proposed by Wang, Xu, Hu [J. Comput. Math, 24(2), 2006], for the singularly perturbed biharmonic equation and the nonlinear von K\'arm\'an equations. The error estimators are proven to be reliable and efficient. Moreover, an adaptive algorithm driven by these error estimators is investigated in numerical experiments.
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Taxonomy
TopicsModel Reduction and Neural Networks · Advanced Numerical Methods in Computational Mathematics · Differential Equations and Numerical Methods