New Advances in Meshless Methods: Coupling Natural Element and Moving Least Squares Techniques
Résumé
We explore in this work the connections between NN and MLS approximations, coming from the introduction of the NN approximation functions as the weights in the scope of MLS. Thus, it is easy to adjust the approximation consistency (with the possibility to enrich the approximation basis with some particular functions describing issues of the searched solution) in the framework of the MLS techniques, precribing exactly essential boundary conditions from the use of the NN approximation as MLS weight. This approach opens, as will be proved in the present paper, the way to a wide range of formulations: (i) NN collocation strategies; (ii) faster natural element discretizations; (iii) Hermite natural element formulations; (iv) hierarchical bubbles functions in the natural element method; and (v) and NN enriched approximations.
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