
J. Rafael Rodríguez GalvánUniversidad de Cádiz | UCA · Department of Mathematics
J. Rafael Rodríguez Galván
Ph.D. Mathematics (Numerical Analysis)
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37
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Publications
Publications (37)
Some new stable finite element (FE) schemes are presented for the hydrostatic Stokes system or primitive equations of the ocean. It is known that the stability of the mixed formulation approximation for primitive equations requires the well-known Ladyzhenskaya--Babuška--Brezzi condition related to the Stokes problem and an extra inf-sup condition r...
The stability of velocity and pressure mixed finite-element approximations in general meshes of the hydrostatic Stokes problem is studied, where two ``inf-sup" conditions appear associated to the two constraints of the problem; namely incompressibility and hydrostatic pressure. Since these two constraints have different properties, it is not easy t...
This paper studies the stability of velocity-pressure mixed approximations of
the Stokes problem when different finite element (FE) spaces for each component
of the velocity field are considered. We consider some new combinations of
continuous FE reducing the number of degrees of freedom in some velocity
components. Although the resulting FE combin...
In this work we present a novel linear and positivity preserving upwind discontinuous Galerkin (DG) approximation of a class of chemotaxis models with damping gradient nonlinearities. In particular, both a local and a nonlocal model including nonlinear diffusion, chemoattraction, chemorepulsion and logistic growth are considered. Some numerical exp...
In this paper, we present a new computational framework using coupled and decoupled approximations for a Cahn-Hilliard-Navier-Stokes model with variable densities and degenerate mobility. In this sense, the coupled approximation is shown to conserve the mass of the fluid, preserve the point-wise bounds of the density and decrease an energy function...
The well-suited discretization of the Keller–Segel equations for chemotaxis has become a very challenging problem due to the convective nature inherent to them. This paper aims to introduce a new upwind, mass-conservative, positive and energy-dissipative discontinuous Galerkin scheme for the Keller–Segel model. This approach is based on the gradien...
he implementation of the wind turbine is a major issue in the wind engineering sector. However, the presence of wind turbines in the lower part of the atmospheric boundary layer (ABL) requires an appropriate study for the simulation of turbulent airflow in the wind farm situated on hilly terrain. The use of precise Computational Fluid Dynamics (CFD...
In this work, we present a modification of the phase-field tumor growth model given in [26] that leads to bounded, more physically meaningful, volume fraction variables. In addition, we develop an upwind discontinuous Galerkin (DG) scheme preserving the mass conservation, pointwise bounds and energy stability of the continuous model. Finally, some...
This article is devoted to the mathematical modeling of migration of neuroblasts, precursor cells of neurons, along the pathway they usually follow before maturing. This pathway is determined mainly by chemotaxis and the heterogeneous mobility of neuroblasts in different regions of the brain. In numerical simulations, the application of novel disco...
The well-suited discretization of the Keller-Segel equations for chemotaxis has become a very challenging problem due to the convective nature inherent to them. This paper aims to introduce a new upwind, mass-conservative, positive and energy-dissipative discontinuous Galerkin scheme for the Keller-Segel model. This approach is based on the gradien...
The design of numerical approximations of the Cahn-Hilliard model preserving the maximum principle is a challenging problem, even more if considering additional transport terms. In this work, we present a new upwind discontinuous Galerkin scheme for the convective Cahn-Hilliard model with degenerate mobility which preserves the maximum principle an...
In this paper we focus on this attraction-repulsion chemotaxis model with consumed signals
\begin{document}$\begin{equation}\label{problem_abstract}\tag{$\Diamond$}\begin{cases}u_t = \Delta u - \chi \nabla \cdot (u \nabla v)+\xi \nabla \cdot (u \nabla w) & \text{ in }~~ \Omega \times (0, T_{max}), \\v_t = \Delta v- uv & \text{ in }~~ \Omega \times...
The design of numerical approximations of the Cahn-Hilliard model preserving the maximum principle is a challenging problem, even more if considering additional transport terms. In this work we present a new upwind Discontinuous Galerkin scheme for the convective Cahn-Hilliard model with degenerate mobility which preserves the maximum principle and...
This paper is devoted to constructing approximate solutions for the classical Keller–Segel model governing chemotaxis. It consists of a system of nonlinear parabolic equations, where the unknowns are the average density of cells (or organisms), which is a conserved variable, and the average density of chemoattractant.
The numerical proposal is made...
We propose a Discontinuous Galerkin (DG) scheme for the Hydrostatic Stokes equations. These equations, related to large-scale PDE models in Oceanography, are characterized by the loss of ellipticity of the vertical momentum equation. This fact provides some interesting challenges, such as the design of stable numerical schemes. The new scheme propo...
A numerical method for approximating weak solutions of an aggregation equation with degenerate diffusion is introduced. The numerical method consists of a finite element method together with a mass lumping technique and an extra stabilizing term plus a semi–implicit Euler time integration. Then we carry out a rigorous passage to the limit as the sp...
This paper is devoted to constructing approximate solutions for the classical Keller--Segel model governing \emph{chemotaxis}. It consists of a system of nonlinear parabolic equations, where the unknowns are the average density of cells (or organisms), which is a conserved variable, and the average density of chemioattranct. The numerical proposal...
This work delves into the numerical approximation of Anisotropic Stokes equations (with small vertical diffusion coefficient), which is a generalization of the Hydrostatic Stokes equations (with zero vertical diffusion). It is known that the Ladyzhenskaya-Babuška-Brezzi condition is not sufficient to stabilize usual finite elements approximations,...
We propose a Discontinuous Galerkin scheme for the numerical solution of the Anisotropic (in particular, Hydrostatic) Stokes equations in Oceanography. The key is the introduction of interior penalties into the usual Stokes bilinear forms and, moreover, in the anisotropy (with respect to the horizontal and vertical directions) of these forms. Using...
We propose a Discontinuous Galerkin (DG) scheme for the numerical solution of the Hydrostatic Stokes equations in Oceanography. This new scheme is based on the introduction of the symmetric interior penalty (SIP) technique for the Hydrostatic Stokes mixed variational formulation. Recent research showed that stability of the mixed formulation of Pri...
We present a review of a theory of stability and accuracy of Finite Element (FE) schemes for the Hydrostatic Stokes system which has been recently developed in Guillén-González and Rodríguez-Galván (Numer Math 130(2):225–256, 2015; SIAM J Numer Anal 53(4):1876–1896, 2015). Moreover, some new numerical results, not previously published, will be show...
A generalization of the classical fuzzy relation equations has been introduced in order to consider any residuated conjunctor. Moreover, these equations can be solved using the theory of a general property-oriented concept lattice.
En este artículo comentamos la experiencia de uso de técnicas y herramientas de desarrollo colaborativo de software en la asignatura " La asignatura se imparte usando aprendizaje basado en proyectos, y gracias a dichas técnicas y herramientas se facilita el seguimiento constante del trabajo de los alumnos por parte del profesor (especialmente al in...
RESUMEN La irrupción de las TIC en nuestra vida cotidiana es un hecho, igual que también lo es en la docencia universitaria. Dentro de las TIC, el software libre está afianzando una posición cada vez más importante tanto en educación como en empresas. Algunas de las características de este tipo de software lo hacen muy interesante para conseguir lo...
Desde los primeros años del siglo XXI, los órganos de gobierno de las universidades españolas están viviendo un creciente interés por el uso del software libre como vía para alcanzar sus principales objetivos. En este artículo se presenta el caso de la Oficina de Software Libre de la Universidad de Cádiz (OSLUCA), con la finalidad de ilustrar la fo...
A lo largo de los últimos años, han ido surgiendo más y más estándares para cubrir la necesidad de interoperabilidad entre diversas organizaciones a lo largo del tiempo, evitando tecnologías cerradas que limiten las opciones de éstas organizaciones. Sin embargo, no basta simplemente con que el estándar sea público para que dicha tecnología se halle...
LAU Proyecto educativo que persigue la integración de las nuevas tecnologías informáticas en la docencia de la Facultad de Ciencias Económicas y Empresariales de la Facultad de Cádiz. Se trata de generar un tipo de docencia a partir de la cual las asignaturas se desarrollen completamente en el aula de ordenadores, integrando el acceso a los recurso...