In the present paper, we delve into the study of nodal systems on the unit circle that meet certain separation properties. Our aim was to study the Hermite interpolation process on the unit circle by using these nodal arrays. The target was to develop the corresponding interpolation theory in order to make practical use of these nodal systems linked to certain mechanical models that fit these distributions.

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Throughout this study, we continue the analysis of a recently found out Gibbs–Wilbraham phenomenon, being related to the behavior of the Lagrange interpolation polynomials of the continuous absolute value function. Our study establishes the error of the Lagrange polynomial interpolants of the function |x| on [−1,1], using Chebyshev and Chebyshev–Lobatto nodal systems with an even number of points. Moreover, with respect to the odd cases, relevant changes in the shape and the extrema of the error are given.

Purpose -A new coupled finite element model has been developed for the joint resolution of both the shallow water equations, that governs the free surface flow, and the groundwater flow equation that governs the motion of water through a porous media. The paper aims to discuss these issues. Design/methodology/approach -The model is based upon two different modules (surface and ground water) previously developed by the authors, that have been validated separately. Findings -The newly developed software allows for the assessment of the fluid flow in natural watersheds taking into account both the surface and the underground flow in the way it really takes place in nature. Originality/value -The main achievement of this work has dealt with the coupling of both models, allowing for a proper moving interface treatment that simulates the actual interaction that takes place between surface and groundwater in natural watersheds.

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