ON THE USE OF A CONTINUOUS STRONG”“FORM RESIDUUM FIELD FOR ERROR ESTIMATION IN SMOOTH GFEM APPROXIMATIONS
DOI:
https://doi.org/10.26512/ripe.v2i14.21365Palavras-chave:
Subdomain error estimators. Implicit residual methods. Ck”“GFEM. Smoothness. Strong-form residuum field.Resumo
This investigation proposes the use of continuous strong”“form residuum fields, obtained through smooth Generalized Finite Element Method (GFEM) , for error estimation in terms of the energy norm. Aspects on the construction of Ck”“GFEM”“based approximation functions (Duarte, Kim & Quaresma, 2006), using domain triangulation, are addressed. It is shown how the smoothness may be exploited in implicit residual algorithms for error estimation since the approximated Ck”“GFEM stress field can be directly continuously differentiated, to verify the equilibrium equations in strong form, locally, and then leading to a continuous residuum field. The subdomain strategy (Barros et al., 2013; Par´es, D´Ä±ez & Huerta, 2006) for implicit error estimation is employed, in such a way the local error problems are defined on the clouds, the patch of elements around the node, through the weighting provided by the Partition of Unity (PoU) functions. Its implementation fits very well into GFEM routines because such strategy is naturally tailored to the nodal enrichment procedure of the method (Barros, Barcellos & Duarte, 2007), producing nodal error indicators. Two types of weighting for the variational residuum functional (Prudhomme et al., 2004; Strouboulis et al., 2006) are tested in order to verify the performance for the effectivity of the nodal indicators and the global estimators. Numerical examples show that both the indicator and the estimator may be effective for two-dimensional linear elastic problems even in the presence of singularities.
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