Abstract
The nodal displacements gain higher convergence rate compared with displacements elsewhere in Finite Element Method (FEM). When the problem is smooth enough, the errors of displacements at element corner nodes can gain convergence order of at most \begin{document}$2m$\end{document} using elements of degree \begin{document}$m$\end{document} in 2D FEM. In this paper, taking the 2D Poisson equation as the model problem and based on an obtained FEM solution, residual nodal load vectors are derived by using super-convergent solutions calculated by Element Energy Projection (EEP) technique. Without changing global stiffness matrices, simple back-substitutions alone would yield nodal displacements of higher convergence rate. Numerical examples show that the nodal displacements can gain super-convergence order of \begin{document}$2m + 2$\end{document} at most when EEP simplified form is used to calculate the residual load vectors. In particular, for linear elements, the accuracy is doubled, and the benefit is very significant.
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