Artículos (Ecuaciones Diferenciales y Análisis Numérico)

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

Examinar

Mostrando 1 - 20 de 1034

Glowinski and numerical control problems
(Académie des sciences, 2023-04-06) Fernández Cara, Enrique; Ecuaciones Diferenciales y Análisis Numérico; FQM131: Ecuaciones diferenciales, Simulación Num. y Desarrollo Software
This paper is devoted to recall several contributions to the numerical control of PDE’s that have origin in Glowinski’s work. I will consider null controllability problems for linear and nonlinear heat equations and some free-boundary systems. We will also deal with some bi-objective optimal control problems. Additionally, some new methods and results will be announced.
Exposición de Méritos de Investigación por el Dr. D. Enrique Fernández Cara, Premio Real Maestranza de Caballería de Sevilla, en el Acto de entrega de los Premios de Investigación de la Academia correspondientes a 1991
(Real Academia Sevillana de Ciencias, 1992) Fernández Cara, Enrique; Ecuaciones Diferenciales y Análisis Numérico; FQM131: Ecuaciones diferenciales, Simulación Num. y Desarrollo Software
Analysis and numerical solution of some minimal time control problems
(Elsevier, 2025-05-22) Fernández Cara, Enrique; Marín Gayte, Irene; Ecuaciones Diferenciales y Análisis Numérico; FQM131: Ecuaciones diferenciales, Simulación Num. y Desarrollo Software
This paper is devoted to the theoretical and numerical analysis of some minimal time control problems associated to linear and nonlinear differential equations. We start by studying simple cases concerning linear and nonlinear ODEs. Then, we deal with the heat equation. In all these situations, we analyze the existence of solutions, we deduce optimality results and we present several algorithms for the computation of optimal controls. Finally, we illustrate the results with several numerical experiments.
General order virtual element approximation for the Smagorinsky turbulence model
(Elsevier, 2026-11) Berrone, Stefano; Cascavita, Karol L; Delgado Ávila, Enrique; Rubino, Samuele; Strazzullo, Maria; Vicini, Fabio; Matemática Aplicada II; Ecuaciones Diferenciales y Análisis Numérico; Ministerio de Ciencia e Innovación (MICIN). España; European Commission (EC). Fondo Europeo de Desarrollo Regional (FEDER)
In this paper, we investigate a Smagorinsky model in a virtual element framework to simulate convection-dominated Navier–Stokes equations. We conduct a two-dimensional numerical investigation to assess the performance of the general order virtual element approximation in this context. First, we examine numerically the convergence of the method with respect to the meshsize to certify the novel virtual element numerical discretization, which includes, for the first time, a discretization of the Smagorinsky term. Moreover, we present a numerical study of a lid-driven cavity for different Reynolds numbers (up to 10000) and meshes (uniform, anisotropic, and isotropic with hanging nodes). The results highlight the main advantage of using the virtual elements method in this context: the isotropic refinement with hanging nodes enhances the accuracy of the solution compared to the anisotropic mesh, uses fewer degrees of freedom with respect to the uniform mesh, and yields the most stable behavior in terms of convergence of the Newton solver.
Stability and convergence at infinite time of several fully discrete schemes for a Ginzburg-Landau model for nematic liquid crystal flows
(AIMS, 2012-08) Guillén González, Francisco Manuel; Goudiaby, Mouhamadou Samsidy; Ecuaciones Diferenciales y Análisis Numérico; FQM131: Ecuaciones diferenciales, Simulación Num. y Desarrollo Software
In this paper, we study a conditional long-time stable fully discrete finite element scheme for a Ginzburg-Landau model for nematic liquid crystal flow. We also obtain its time asymptotic convergence (when number of time steps go to infinity, fixed time step and mesh size) towards a unique critical point of the elastic energy subject to the finite element subspace. Finally, we estimate some convergence rates towards this limit critical point. To prove convergence of the whole sequence, a Lojasiewicz type inequality is used.
Splitting schemes for a Navier-Stokes-Cahn-Hilliard model for two fluids with different densities
(Global Science Press, 2014-09-03) Guillén González, Francisco Manuel; Tierra, Giordano; Ecuaciones Diferenciales y Análisis Numérico; FQM131: Ecuaciones diferenciales, Simulación Num. y Desarrollo Software
In this work, we focus on designing efficient numerical schemes to approximate a thermodynamically consistent Navier-Stokes/Cahn-Hilliard problem given in [3] modeling the mixture of two incompressible fluids with different densities. The model is based on a diffuse-interface phase-field approach that is able to describe topological transitions like droplet coalescence or droplet break-up in a natural way. We present a splitting scheme, decoupling computations of the Navier-Stokes part from the Cahn-Hilliard one, which is unconditionally energy-stable up to the choice of the potential approximation. Some numerical experiments are carried out to validate the correctness and the accuracy of the scheme, and to study the sensitivity of the scheme with respect to different physical parameters.
Spatial error estimates for a finite element viscosity-splitting scheme for the Navier-Stokes equations
(Global Science Press, 2013) Guillén González, Francisco Manuel; Redondo Neble, María Victoria; Ecuaciones Diferenciales y Análisis Numérico; FQM131: Ecuaciones diferenciales, Simulación Num. y Desarrollo Software
In this paper, we obtain optimal first order error estimates for a fully discrete fractional-step scheme applied to the Navier-Stokes equations. This scheme uses decomposition of the viscosity in time and finite elements (FE) in space. In [15], optimal first order error estimates (for velocity and pressure) for the corresponding time-discrete scheme were obtained, using in particular H2XH1 estimates for the approximations of the velocity and pressure. Now, we use this time-discrete scheme as an auxiliary problem to study a fully discrete finite element scheme, obtaining optimal first order approximation for velocity and pressure with respect to the max-norm in time and the H1XL2-norm in space. The proof of these error estimates are based on three main points: a) provide some new estimates for the time-discrete scheme (not proved in [15]) which must be now used, b) give a discrete version of the H2XH1 estimates in FE spaces, using stability in the W1,6XL6-norm of the FE Stokes projector, and c) the use of a weight function vanishing at initial time will let to hold the error estimates without imposing global compatibility for the exact solution.
Second order schemes and time-step adaptivity for Allen-Cahn and Cahn-Hilliard models
(Elsevier, 2014-07-19) Guillén González, Francisco Manuel; Tierra, Giordano; Ecuaciones Diferenciales y Análisis Numérico; FQM131: Ecuaciones diferenciales, Simulación Num. y Desarrollo Software
In this paper, we focus on efficient second-order in time approximations of the Allen–Cahn and Cahn–Hilliard equations. First of all, we present the equations, generic second-order schemes (based on a mid-point approximation of the diffusion term) and some schemes already introduced in the literature. Then, we propose new ways of deriving second-order in time approximations of the potential term (starting from the main schemes introduced in Guillén-González and Tierra (2013)), yielding to new second-order schemes. For these schemes and other second-order schemes previously introduced in the literature, we study the constraints on the physical and discrete parameters that can appear to assure the energy-stability, unique solvability and, in the case of nonlinear schemes, the convergence of Newton’s method to the nonlinear schemes. Moreover, in order to save computational cost we have developed a new adaptive time-stepping algorithm based on the numerical dissipation introduced in the discrete energy law in each time step. Finally, we compare the behaviour of the schemes and the effectiveness of the adaptive time-stepping algorithm through several computational experiments.
Reproductive solution of a second-grade fluid system
(Elsevier, 2010-07-22) Friz, Luis; Guillén González, Francisco Manuel; Rojas Medar, Marko Antonio; Ecuaciones Diferenciales y Análisis Numérico; FQM131: Ecuaciones diferenciales, Simulación Num. y Desarrollo Software
We treat the existence and uniqueness of reproductive solution (weak time-periodic solution) of a second-grade fluid system for small enough source terms, by using the Galerkin approximation method and compactness arguments.
Property-preserving numerical approximation of a Cahn–Hilliard–Navier–Stokes model with variable density and degenerate mobility
(Elsevier, 2025-03) Acosta Soba, Daniel; Guillén González, Francisco Manuel; Rodríguez Galván, José Rafael; Wang, Jin; Ecuaciones Diferenciales y Análisis Numérico; FQM131: Ecuaciones diferenciales, Simulación Num. y Desarrollo Software
In this paper, we present a new computational framework to approximate a Cahn–Hilliard–Navier–Stokes model with variable density and degenerate mobility that preserves the mass of the mixture, the pointwise bounds of the density and the decreasing energy. This numerical scheme is based on a finite element approximation for the Navier–Stokes fluid flow with discontinuous pressure and an upwind discontinuous Galerkin scheme for the Cahn–Hilliard part. Finally, several numerical experiments such as a convergence test and some well-known benchmark problems are conducted.
Optimal first-order error estimates of a fully segregated scheme for the Navier-Stokes equations
(Elsevier, 2017-03-10) Guillén González, Francisco Manuel; Redondo Neble, María Victoria; Ecuaciones Diferenciales y Análisis Numérico; FQM131: Ecuaciones diferenciales, Simulación Num. y Desarrollo Software
A first-order linear fully discrete scheme is studied for the incompressible time-dependent Navier–Stokes equations in three-dimensional domains. This scheme is based on an incremental pressure projection method and decouples each component of the velocity and the pressure, solving in each time step, a linear convection–diffusion problem for each component of the velocity and a Poisson–Neumann problem for the pressure. Using an inf–sup stable and continuous finite-elements approach of order 0 (h) in space, unconditional optimal error estimates of order 0 (k + h) are deduced for velocity and pressure (without imposing constraints on the mesh size h and the time step k). Finally, some numerical results are performed to validate the theoretical analysis, and also to compare the studied scheme with other current first-order segregated schemes.
Optimal Control Related to Weak Solutions of a Chemotaxis-Consumption Model
(Springer, 2024-03-20) Corrêa Vianna Filho, André Luiz; Guillén González, Francisco Manuel; Ecuaciones Diferenciales y Análisis Numérico; FQM131: Ecuaciones diferenciales, Simulación Num. y Desarrollo Software
In the present work we investigate an optimal control problem related to the following chemotaxis-consumption model in a bounded domain Ω ⊂ R3: atu - Au = ........... , with s≥1, endowed with isolated boundary conditions and initial conditions for (u, v), being u the cell density, v the chemical concentration and f the control acting in the v-equation through the bilinear term fv1Ωc, in a subdomain Ωc ⊂ Ω. We address the existence of optimal control restricted to a weak solution setting, where, in particular, uniqueness of state (u, v) given a control f is not clear. Then by considering weak solutions satisfying an adequate energy inequality, we prove the existence of optimal control subject to uniformly bounded controls. Finally, we discuss the relation between the considered control problem and two other related ones, where the existence of optimal solution can not be proved.
Global classical solutions for a two-dimensional Keller-Segel-Navier-Stokes system of potential type
(Springer, 2026-02-28) Barbosa, Daniel Moraes; Guillén González, Francisco Manuel; Planas, Gabriela; Ecuaciones Diferenciales y Análisis Numérico; FQM131: Ecuaciones diferenciales, Simulación Num. y Desarrollo Software
The present work deals with a Keller-Segel-Navier-Stokes system in two-dimensional domains, which involves a cell density, an attractive chemical signal consumed by the cells, and a repulsive one produced by the cells. Potential consumption and production rates jointly with a generalized logistic law for the cells are considered, under non-flux boundary conditions for cell and chemical variables and a Dirichlet boundary condition for the velocity field. We establish the existence of global classical solutions for the system under some constraints related to the rates of attraction, consumption, and logistic competition with chemotactic sensitivities.
An Unconditionally Energy Stable and Positive Upwind DG Scheme for the Keller–Segel Model
(Springer, 2023-09-09) Acosta Soba, Daniel; Guillén González, Francisco Manuel; Rodríguez Galván, José Rafael; Ecuaciones Diferenciales y Análisis Numérico; FQM131: Ecuaciones diferenciales, Simulación Num. y Desarrollo Software
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 gradient-flow structure of the equations. In addition, we show some numerical experiments in accordance with the aforementioned properties of the discretization. The numerical results obtained emphasize the really good behaviour of the approximation in the case of chemotactic collapse, where very steep gradients appear.
A convergent time scheme for a chemotaxis-fluids model with potential consumption
(EDP Sciences, 2025-12-01) Barbosa, Daniel Moraes; Guillén González, Francisco Manuel; Planas, Gabriela; Ecuaciones Diferenciales y Análisis Numérico; FQM131: Ecuaciones diferenciales, Simulación Num. y Desarrollo Software
The present work deals with a Keller–Segel–Navier–Stokes system with potential consumption, under homogeneous Neumann boundary conditions for cell density and chemical signal, and Dirichlet type for the velocity field, over a bounded three-dimensional domain. The paper aims to develop a time discretization scheme converging to weak solutions of the system, which are uniformly bounded at infinite time. While global existence results are already known for simplified cases, either in absence of fluid flow or for linear consumption, the existence of global weak solutions for the fully coupled system with potential consumption has remained as an open problem.
Survey on chemostat models with bounded random input flow
(AIMS, 2021-03-19) Caraballo Garrido, Tomás; López de la Cruz, Javier; Ecuaciones Diferenciales y Análisis Numérico; FQM314: Análisis Estocástico de Sistemas Diferenciales
In this paper we study some chemostat models with random bounded fluctuations on the input flow. We start with the classical chemostat system and obtain new models incorporating, for instance, wall growth and di erent consumption functions, motivated by phenomena in real devices. In every case, we prove existence and uniqueness of positive global solution, existence of deterministic absorbing and attracting sets and we investigate the internal structure of the attracting sets to obtain detailed information about the long-time dynamics of the systems. This allows us to provide conditions under which either extinction or persistence of the species is ensured, the main goal for practitioners. In addition, we provide several numerical simulations to support the theoretical results.
Stability with respect to a part of the variables of stochastic nonlinear systems driven by G-Brownian motion
(Taylor & Francis, 2022-05-03) Caraballo Garrido, Tomás; Ezzine, Faten; Hammami, Mohamed Ali; Ecuaciones Diferenciales y Análisis Numérico; FQM314: Análisis Estocástico de Sistemas Diferenciales
In this paper, we investigate the pth moment exponential stability of stochastic differential equations driven by G-Brownian motion (G-SDEs) with respect to a part of the variables by means of the G-Lyapunov functions and recently developed Itô's calculus for SDEs driven by G-Brownian motion, as well as Gronwall's inequalities. We establish sufficient conditions to ensure the quasi sure exponential stability of stochastic differential equations perturbed by G-Brownian motion with respect to a part of the variables. Some illustrative examples to show the usefulness of the stability with respect to a part of the variables notion are also provided.
Robust dynamics for compact-valued cocycle of stochastic sShrödinger lattice equation with Wong-Zakai noise
(AIMS, 2025-09-05) Wang, Fengling; Caraballo Garrido, Tomás; Li, Yangrong; Ecuaciones Diferenciales y Análisis Numérico; FQM314: Análisis Estocástico de Sistemas Diferenciales
We study Wong-Zakai approximations and random attractors of complex stochastic Schr¨odinger lattice systems driven by non-Lipschitz sources and nonlinear diffusion noise. The non-Lipschitz continuity of both drift and diffusion terms leads to possible multi-solutions and hence the lattice equation generates a multi-valued cocycle, which is proved to be measurable and compact-valued. We first show the existence of a pullback attractor for the approximate system, and then apply the weak upper semicontinuity of multi-valued functions and a countable decomposition of the Wiener probability space to prove the measurability of the pullback attractor as well as the multi-valued cocycle in the original probability space (rather than only in its completion). We finally establish the upper semi-convergence of random attractors from the approximate system to the original Schr¨odinger lattice system driven by linear multiplicative white noise, as the step size of Wong-Zakai noise tends to zero.
Pullback attractors and statistical solutions for the lattice Zakharov equations on time-dependent spaces
(AIMS, 2026-02-04) Li, Anran; Zhao, Caidi; Caraballo Garrido, Tomás; Ecuaciones Diferenciales y Análisis Numérico; FQM314: Análisis Estocástico de Sistemas Diferenciales
In this paper, the authors investigate the probability distribution of solutions within the timedependent phase spaces for the lattice Zakharov equations with varying coefficients via the pullback attractors and the notion of generalized Banach limits. They firstly show that the addressed initial value problem is globally well-posed and prove that the related evolution process has a time-dependent pullback attractor on the time-dependent phase spaces. Then they construct a family of invariant Borel probability measures with supports contained in the pullback attractor. Furthermore, they prove that the constructed family of invariant measures is a statistical solution for the addressed lattice Zakharov equations and that Liouville’s theorem holds true.
Preface to the special issue "Dynamics and control in distributed systems"
(AIMS, 2024-03) Caraballo Garrido, Tomás; Kapustyan, Oleksiy V.; Kasyanov, Pavlo O.; Valero, José; Zgurovsky, Michael; Ecuaciones Diferenciales y Análisis Numérico; FQM314: Análisis Estocástico de Sistemas Diferenciales

Examinar

Envíos recientes