Abstract
The motion equation is transformed into a system of the first order differential equations (ODEs); and by using the linear finite element of the Galerkin type, the explicit recurrence formula is derived with an accuracy of \begin{document}$O({h^2})$\end{document} . By using the element energy projection (EEP) technique, the nodal accuracy recovery approach improves the recurrence formula to yield a nodal accuracy of \begin{document}$O({h^4})$\end{document} . Further, the stability property and convergence orders are analyzed mathematically with a given scheme of adaptive step-size. Finally, the given numerical examples justify that the proposed approach is a simple and effective method.
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