Artículos (Ecuaciones Diferenciales y Análisis Numérico)

URI permanente para esta colecciónhttps://hdl.handle.net/11441/10834

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A three population Lotka-Volterra competition model with two populations interacting through an interface
(2026-02-01) Álvarez Caudevilla, Pablo; Brändle Cerqueira, Cristina; Molina Becerra, Mónica; Suárez Fernández, Antonio; Matemática Aplicada II (ETSI); Ecuaciones Diferenciales y Análisis Numérico; Ministerio de Ciencia, Innovación y Universidades (MICIU). España; TIC130: Investigación en Sistemas Dinámicos en Ingeniería; FQM131: Ecuaciones diferenciales, Simulación Num. y Desarrollo Software
In this work we consider three species competing with each other in the same habitat. One of the species lives in the entire habitat, competing with the other two species, while the other two inhabit two disjoint regions of the habitat. These two populations just interact on a region/interface which acts as a geographical barrier. This barrier condition causes a drastic change in species behaviour compared to the classical Lotka-Volterra competitive model, showing very rich and new different situations depending on the several parameters involved in the system.
Remarks on exponential attractors for a non-autonomous PDE with H^(-1)-valued forces
(AIMS, 2025-01) Aguilar Reyes, Álvaro; Marín Rubio, Pedro; Ecuaciones Diferenciales y Análisis Numérico; FQM314: Análisis Estocástico de Sistemas Diferenciales
A reaction-diffusion problem with time-dependent force with values in is considered. Some results ensuring the existence of pullback exponential attractors are established, combining some classical and more recent developments on the topic. Two different sets of assumptions are considered. One involves translation bounded forces. The second one allows time-exponential growth in the past.
Weak global attractor for the 3D-Navier–Stokes equations via the globally modified Navier–Stokes equations
(Springer, 2024-11-26) Bortolan, Matheus Cheque; Carvalho, Alexandre Nolasco; Marín Rubio, Pedro; Valero, José; Ecuaciones Diferenciales y Análisis Numérico; FQM314: Análisis Estocástico de Sistemas Diferenciales
In this paper, we obtain the existence of a weak global attractor for the three-dimensional Navier–Stokes equations, that is, a weakly compact set with an invariance property, that uniformly attracts solutions, with respect to the weak topology, for initial data in bounded sets. To that end, we define this weak global attractor in terms of limits of solutions of the globally modified Navier–Stokes equations in the weak topology. We use the theory of semilinear parabolic equations and -regularity to obtain the local well-posedness for the globally modified Navier–Stokes equations, the existence of the global attractor and its regularity.
Remarks on non-homogeneous Cauchy problems with time-dependent generators
(Springer, 2025-03-24) Marín Rubio, Pedro; Seminario Huertas, Paulo Nicanor; Ecuaciones Diferenciales y Análisis Numérico; FQM314: Análisis Estocástico de Sistemas Diferenciales
In this paper it is studied the well-posedness in several senses for non-homogeneous Cauchy problems where the infinitesimal generator depends on the time parameter. More specifically, we analyze the existence of classical, mild and weak solutions and their relationships. Thanks to uniqueness arguments, mild solutions are proved to satisfy a classical variational formulation. Finally, these results are applied to a thermoelastic plate model where the thermal part is of Cattaneo type and all the physical coefficients depend on time.
Mathematical Modeling of Neuroblast Migration Toward the Olfactory Bulb
(Elsevier, 2025) Acosta Soba, Daniel; Castro, Carmen; Geribaldi Doldán, Noelia; Guillén González, Francisco Manuel; Núñez Abades, Pedro Antonio; Ortega Román, Noelia; Pérez García, Patricia; Rodríguez Galván, J. Rafael; Fisiología; Ecuaciones Diferenciales y Análisis Numérico; Ministerio de Ciencia, Innovación y Universidades (MICIU). España; European Commission (EC). Fondo Europeo de Desarrollo Regional (FEDER); Universidad de Cádiz; University of Tennessee; Junta de Andalucía
This article is devoted to the mathematical modeling of the migration of neuroblasts, precursor cells of neurons, along the Rostral Migratory Stream (RMS), the pathway they usually follow before maturing. According to our model, this way is determined mainly by attraction forces to the olfactory bulb, and also by the heterogeneous mobility of neuroblasts in different regions of the brain. Carefully identifying them as solutions to partial differential equations allows us to determine the movement of neuroblasts along the RMS in a realistic fashion. For solving the equations we develop numerical schemes where the application of novel discontinuous Galerkin methods allows to maintain the properties of the continuous model such as the maximum principle. We present some successful computer tests including parameter adjustment to fit real data from rodent brains.
On the null controllability of a one-dimensional fluid–solid interaction model
(Académie des sciences, 2003-11-05) Doubova Krasotchenko, Anna; Fernández Cara, Enrique; Ecuaciones Diferenciales y Análisis Numérico; FQM131: Ecuaciones diferenciales, Simulación Num. y Desarrollo Software
We analyze the null controllability of a one-dimensional nonlinear system which models the interaction of a fluid and a particle. The fluid is governed by the Burgers equation and the control is exerted on the boundary points. We present two main results: the global null controllability of a linearized system and the local null controllability of the nonlinear original model. The proofs rely on appropriate global Carleman inequalities and fixed point arguments.
A non-overlapping domain decomposition method for the Stokes equations via a penalti term on the interface
(Académie des sciences, 2002-02-01) Chacón Rebollo, Tomás; Chacón Vera, Eliseo; Ecuaciones Diferenciales y Análisis Numérico
The purpose of this Note is to perform a theoretical analysis of the domain decomposition method introduced in [2]. We motivate and introduce an improvement of this method and carry out the analysis when it is applied to solving the Stokes equations. Our method is based on a penalty term on the interface between subdomains that enforces the appropriate transmission conditions and may be seen as variation of the Robin method. We obtain strong convergence results for velocity and pressure in the standard H1 and L2 norms and precise rates of convergence, together with error estimates. These error estimates are of optimal order with respect to the precision of the interpolation. We conclude with some numerical tests.
Derivation of the k-epsilon model for locally homogeneous turbulence by homogenization techniques
(Académie des sciences, 2003-09-15) Chacón Rebollo, Tomás; Franco Coronil, Daniel; Ecuaciones Diferenciales y Análisis Numérico; FQM120: Modelado Matemático y Simulación de Sistemas Medioambientales
We derive the incompressible and compressible k–ε model for locally homogeneous turbulence. The model is rigorously derived on formal mathematical grounds using the MPP modelling technique. This lets us calculate by either analytical or numerical means the closure constants of the model.
Error bounds in high-order Sobolev norms for POD expansions of parameterized transient temperaturas Estimations d'erreur d'ordre élevé pour la décomposition POD appliquée à l'équation de la chaleur parametrisée
(Elsevier, 2017-04-13) Azaïez, Mejdi; Ben Belgacem, Faker; Chacón Rebollo, Tomás; Gómez Mármol, María Macarena; Sánchez Muñoz, Isabel María; Ecuaciones Diferenciales y Análisis Numérico; FQM120: Modelado Matemático y Simulación de Sistemas Medioambientales
In this work, we analyze the convergence of the POD expansion for the solution to the heat conduction parameterized with respect to the thermal conductivity coefficient. We obtain error bounds for the POD approximation in high-order norms in space that assure an exponential rate of convergence, uniformly with respect to the parameter whenever it remains within a compact set of positive numbers. We present some numerical tests that confirm this theoretical accuracy.
A Petrov–Galerkin multilayer discretization to second order elliptic boundary value problems
(Elsevier, 2019-06-15) Chacón Rebollo, Tomás; Franco Coronil, Daniel; Hecht, Frédéric; Ecuaciones Diferenciales y Análisis Numérico; FQM120: Modelado Matemático y Simulación de Sistemas Medioambientales
We study in this paper a multilayer discretization of second order elliptic problems, aimed at providing reliable multilayer discretizations of shallow fluid flow problems with diffusive effects. This discretization is based upon the formulation by transposition of the equations. It is a Petrov–Galerkin discretization in which the trial functions are piecewise constant per horizontal layers, while the test functions are continuous piecewise linear, on a vertically shifted grid. We prove the well posedness and optimal error order estimates for this discretization in natural norms, based upon specific inf–sup conditions. We present some numerical tests with parallel computing of the solution based upon the multilayer structure of the discretization, for academic problems with smooth solutions, with results in full agreement with the theory developed.
Anisotropic VMS solution of advection–diffusion problems by spectral approximation of sub-grid scales
(Elsevier, 2020-12-15) Chacón Rebollo, Tomás; Fernández García, Soledad; Gómez Mármol, María Macarena; Ecuaciones Diferenciales y Análisis Numérico; FQM120: Modelado Matemático y Simulación de Sistemas Medioambientales
In this article, we extend the Variational Multi-scale method with spectral approximation of the sub-scales to two-dimensional advection–diffusion problems. The spectral VMS method is cast for low-order elements as a standard VMS method with specific stabilized coefficients, that are anisotropic in the sense that they depend on two grid Péclet numbers, each associated to a component of the advection velocity. We compute the stabilized coefficients for grids of isosceles right triangles and right quadrilaterals, based upon the explicit computation of the eigen-pairs of the advection–diffusion operator with Dirichlet boundary conditions. To reduce the computing time, the stabilized coefficients are pre-computed at the nodes of a grid in an off-line step, and then interpolated by a fast procedure in the on-line computation. Finally, we present some numerical tests in order to compare our results with those provided by other stabilization coefficients, both isotropic and anisotropic ones. We consider tests for advection–diffusion equations with constant and anisotropic velocities, as well as tests in structured and unstructured meshes. We also test the method for the solution of Navier–Stokes equations. We observe a relevant accuracy gain for moderately large grid Péclet numbers for variable advection velocity.
Preface special issue ICIAM 2019
(Elsevier, 2022-08-24) Vázquez Cendón, Carlos; Vázquez Cendón, Carlos; Ecuaciones Diferenciales y Análisis Numérico; FQM120: Modelado Matemático y Simulación de Sistemas Medioambientales
This special issue of SeMA Journal is closely related with the 9thInternational Congress in Industrial and Applied Mathematics, ICIAM2019, held in Valencia (Spain) on July, 2019. More precisely, this Open Access volume contains reviews and original articles written by some of the top-level scientists who received different awards or delivered special talks during ICIAM2019, who kindly accepted to submit them to SeMA Journal.
Least-squares pressure recovery in reduced order methods for incompressible flows
(Elsevier, 2024-12-15) Azaïez, Mejdi; Chacón Rebollo, Tomás; Oulghelou, M.; Sánchez Muñoz, Isabel María; Ecuaciones Diferenciales y Análisis Numérico; FQM120: Modelado Matemático y Simulación de Sistemas Medioambientales
In this work, we introduce a method to recover the reduced pressure for Reduced Order Models (ROMs) of incompressible flows. The pressure is obtained as the least-squares minimum of the residual of the reduced velocity with respect to a dual norm. We prove that this procedure provides a unique solution whenever the full-order pair of velocity-pressure spaces is inf-sup stable. We also prove that the proposed method is equivalent to solving the reduced mixed problem with reduced velocity basis enriched with the supremizers of the reduced pressure gradients. Optimal error estimates for the reduced pressure are obtained for general incompressible flow equations and specifically, for the transient Navier-Stokes equations. We also perform some numerical tests for the flow past a cylinder and the lid-driven cavity flow which confirm the theoretical expectations, and show an improved convergence with respect to other pressure recovery methods.
Hybrid reduced order model for heat exchange in concentrated solar power receivers
(AIMS, 2024-12-09) Chacón Rebollo, Tomás; Núñez Fernández, Carlos; Rubino, Samuele; Valverde, Juan S.; Ecuaciones Diferenciales y Análisis Numérico; FQM120: Modelado Matemático y Simulación de Sistemas Medioambientales
We present a proper orthogonal decomposition-reduced order model (POD-ROM) approach to the heat transfer fluid (HTF) problem in the modeling of concentrated solar power (CSP) tower receivers. We build a 3D hybrid POD-ROM combining two techniques: an intrusive one for the temperature field, and a non-intrusive data-driven one for the velocity field. Additionally, two different software are employed: ANSYS Fluent, which is a commercial software, and FreeFEM, an open-source software. Accurate results are obtained with relative errors of 10-3 and a speedup of 4 orders of magnitude.
Data-driven stabilized finite element solution of advection-dominated flow problems
(Elsevier, 2024-07-23) Chacón Rebollo, Tomás; Franco Coronil, Daniel; Ecuaciones Diferenciales y Análisis Numérico; FQM120: Modelado Matemático y Simulación de Sistemas Medioambientales
In this article, we address the solution of advection-dominated flow problems by stabilized methods, by means of data-driven least-squares computed stabilized coefficients. As main methodological tool, we introduce a data-driven off-line/on-line strategy to compute them with low computational cost. We compare the errors provided by the data-driven stabilized coefficients to those provided by several previously established stabilized coefficients within the solution of advection–diffusion and Navier–Stokes flows, on structured and un-structured grids, with Lagrange Finite Elements up to third degree of interpolation. We obtain substantial error improvements for high-order finite element interpolation. We conclude that the data-driven procedure is a rewarding procedure, worth to be applied to general stabilized solutions of general flow problems.
Variational multiscale evolve and filter strategies for convection-dominated flows
(Elsevier, 2025-04-01) Strazzullo, Maria; Ballarin, Francesco; Iliescu, Traian; Chacón Rebollo, Tomás; Ecuaciones Diferenciales y Análisis Numérico; FQM120: Modelado Matemático y Simulación de Sistemas Medioambientales
The evolve-filter (EF) model is a filter-based numerical stabilization for under-resolved convection-dominated flows. EF is a simple, modular, and effective strategy for both full-order models (FOMs) and reduced-order models (ROMs). It is well-known, however, that when the filter radius is too large, EF can be overdiffusive and yield inaccurate results. To alleviate this, EF is usually supplemented with a relaxation step. The relaxation parameter, however, is very sensitive with respect to the model parameters. In this paper, we propose a novel strategy to alleviate the EF overdiffusivity. Specifically, we leverage the variational multiscale (VMS) framework to separate the large resolved scales from the small resolved scales in the evolved velocity, and we use the filtered small scales to correct the large scales. Furthermore, in the new VMS-EF strategy, we use two different approaches to decompose the evolved velocity: the VMS Evolve-Filter-Filter-Correct (VMS-EFFC) and the VMS Evolve-Postprocess-Filter-Correct (VMS-EPFC) algorithms. The new VMS-based algorithms yield significantly more accurate results than the standard EF in both the FOM and the ROM simulations of a flow past a cylinder at Reynolds number Re = 1000.
Space-time mesh adaptation for the VMS-Smagorinsky modeling of high Reynolds number flows
(Elsevier, 2025-09-15) Temellini, Erika; Ferro, Nicola; Stabile, Giovanni; Delgado Ávila, Enrique; Chacón Rebollo, Tomás; Perotto, Simona; Ecuaciones Diferenciales y Análisis Numérico
Traditional methods, such as Reynolds-Averaged Navier-Stokes (RANS) equations and Large Eddy Simulations (LES), provide consolidated tools for the numerical approximation of high Reynolds number flows in a wide range of applications - from green energy to industrial design. In general, RANS modeling is practical when the main interest is the time-averaged flow behavior. LES equations offer detailed insights into flow dynamics and a more accurate solution, but the high computational demand necessitates innovative strategies to reduce costs while maintaining precision. In this study, we enhance the Variational MultiScale (VMS)-Smagorinsky LES model by relying on an adaptive discretization strategy in both space and time, driven by a recovery-based a posteriori error analysis. We assess the effectiveness of the approach in capturing flow characteristics across a wide range of Reynolds numbers through benchmark tests.
Self-Adjusting Multi-Rate Runge-Kutta Methods: Analysis and Efficient Implementation in An Open Source Framework
(Springer, 2025-09-13) Bachmann, Bernhard; Bonaventura, Francesco; Casella, Francesco; Fernández García, Soledad; Gómez Mármol, María Macarena; Hannebohm, Philip; Ecuaciones Diferenciales y Análisis Numérico; FQM120: Modelado Matemático y Simulación de Sistemas Medioambientales
We present an approach for the efficient implementation of self-adjusting multi-rate Runge-Kutta methods and we introduce a novel stability analysis, that covers the multi-rate extensions of all standard Runge-Kutta methods and allows to assess the impact of different interpolation methods for the latent variables and of the use of an arbitrary number of sub-steps for the active variables. The stability analysis applies successfully to the model problem typically used in the literature for multi-rate methods. Furthermore, we also propose a physically motivated model problem that can be used to assess stability to problems with purely imaginary eigenvalues and in situations closer to those arising in applications. Finally, we present an efficient implementation of multi-rate Runge-Kutta methods in the framework of the OpenModelica open-source modelling and simulation software. Results of several numerical experiments, performed with this implementation of the proposed methods, demonstrate the efficiency gains deriving from the use of the proposed multi-rate approach for physical modelling problems with multiple time scales.
On the Navier condition for viscous fluids in rough domains
(Springer, 2012) Casado Díaz, Juan; Luna Laynez, Manuel; Suárez Grau, Francisco Javier; Ecuaciones Diferenciales y Análisis Numérico; Ministerio de Ciencia e Innovación (MICIN). España; FQM309: Control y Homogeneización de Ecuaciones en Derivadas Parciales
Effects of rough boundary on the heat transfer in a thin film flow
(Elsevier, 2013-06-13) Pazanin, Igor; Suárez Grau, Francisco Javier; Ecuaciones Diferenciales y Análisis Numérico; Ministry of Science, Education and Sports, Republic of Croatia; Ministerio de Economía y Competitividad (MINECO). España; FQM309: Control y Homogeneización de Ecuaciones en Derivadas Parciales
In this Note a heat flow through a rough thin domain filled with fluid (lubricant) is studied. Domain's thickness is considered as the small parameter $\varepsilon$, while the roughness is defined by a periodical function with period of order $\varepsilon^2$. We assume that the lubricant is cooled by the exterior medium and we describe the heat exchange on the rough part of the boundary by the Newton's cooling law. Depending on the magnitude of the heat transfer coefficient with respect to $\varepsilon$, we obtain three different macroscopic models via formal asymptotic analysis. We identify the critical case explicitly acknowledging both roughness-induced effects and the effects of surrounding medium on the heat transfer at main order. We illustrate the obtained results by some numerical simulations.

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