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This study aims to propose and numerically assess different ways of discretising a very weak formulation of the Poisson problem.

We use integration by parts twice to shift smoothness requirements to the test functions, thereby allowing low-regularity data and solutions.

Various conforming discretisations are presented and tested, with numerical results indicating good accuracy and stability in different types of problems.

This is one of the first articles to propose and test concrete discretisations for very weak variational formulations in primal form. The numerical results, which include a problem based on real MRI data, indicate the potential of very weak finite element methods for tackling problems with low regularity.

This paper aims to investigate the hydrodynamic instability properties of a mixed convection flow of nanofluid in a porous channel.

The treated single-phase nanofluid is a suspension consisting of water as the working fluid and alumina as a nanoparticle. The anisotropy of the porous medium and the effects of the inclination of the magnetic field are highlighted. The effects of viscous dissipation and thermal radiation are incorporated into the energy equation. The eigenvalue equation system resulting from the stability analysis is processed numerically by the spectral collocation method.

Analysis of the results in terms of growth rate reveals that increasing the volume fraction of nanoparticles increases the critical Reynolds number. Parameters such as the mechanical anisotropy parameter and Richardson number have a destabilizing effect. The Hartmann number, permeability parameter, magnetic field inclination, Prandtl number, wave number and thermal radiation parameter showed a stabilizing effect. The Eckert number has a negligible effect on the growth rate of the disturbances.

Linear stability analysis of Magnetohydrodynamics (MHD) mixed convection flow of a radiating nanofluid in porous channel in presence of viscous dissipation.

Climate change is a problem that concerns all of us. Despite the information produced by organizations such as the Expert Team on Climate Change Detection and Indices and the United Nations, only a few cities have been planned taking into account the climate changes indices. This paper aims to study climatic variations, how climate conditions might change in the future and how these changes will affect the activities and living conditions in cities, specifically focusing on Mexico city.

In this approach, two distinct machine learning regression models, k-Nearest Neighbors and Support Vector Regression, were used to predict variations in climate change indices within select urban areas of Mexico city. The calculated indices are based on maximum, minimum and average temperature data collected from the National Water Commission in Mexico and the Scientific Research Center of Ensenada. The methodology involves pre-processing temperature data to create a training data set for regression algorithms. It then computes predictions for each temperature parameter and ultimately assesses the performance of these algorithms based on precision metrics scores.

This paper combines a geospatial perspective with computational tools and machine learning algorithms. Among the two regression algorithms used, it was observed that k-Nearest Neighbors produced superior results, achieving an R² score of 0.99, in contrast to Support Vector Regression, which yielded an R² score of 0.74.

The full potential of machine learning algorithms has not been fully harnessed for predicting climate indices. This paper also identifies the strengths and weaknesses of each algorithm and how the generated estimations can then be considered in the decision-making process.