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Artículo
Numerical methods for solving the Cahn-Hilliard equation and its applicability to related Energy-based models
(Springer, 2015-04)
In this paper, we review some numerical methods presented in the literature in the last years to approximate the Cahn-Hilliard equation. Our aim is to compare the main properties of each one of the approaches to try to ...
Artículo
Stabilized schemes for the hydrostatic Stokes equations
(Society for Industrial and Applied Mathematics, 2015)
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 ...
Artículo
Unconditionally energy stable fully discrete schemes for a chemo-repulsion model
(American Mathematical Society, 2019-09)
This work is devoted to studying unconditionally energy stable and mass-conservative numerical schemes for the following repulsive-productive chemotaxis model: find u ≥ 0, the cell density, and v ≥ 0, the chemical ...
Artículo
Convergence to equilibrium of global weak solutions for a Cahn-Hilliard-Navier-Stokes vesicle model
(Springer, 2019-08)
In this paper, we introduce a model describing the dynamic of vesicle membranes within an incompressible viscous fluid in 3D domains. The system consists of the NavierStokes equations, with an extra stress tensor depending ...
Artículo
Conditional stability and convergence of a fully discrete scheme for three-dimensional Navier–Stokes equations with mass diffusion
(Society for Industrial and Applied Mathematics, 2008)
We construct a fully discrete numerical scheme for three-dimensional incompressible fluids with mass diffusion (in density-velocity-pressure formulation), also called the Kazhikhov–Smagulov model. We will prove conditional ...
Artículo
Método de elementos finitos para la aproximación de un modelo de cristales líquidos nemáticos
(Sociedad Española de Matemática Aplicada, 2009)
En esta charla analizamos la aproximación numérica con elementos finitos en espacio y diferencias finitas en tiempo de un modelo de cristales líquidos nemáticos (de tipo Eriksen-Leslie) y de un modelo penalizado de tipo ...
Artículo
On the singular times of fluids with nonlinear viscosity
(Elsevier, 2001-11-15)
Artículo
Convergence to equilibrium for smectic-A liquid crystals in 3D domains without constraints for the viscosity
(Elsevier, 2014-06)
In this paper, we focus on a smectic-A liquid crystal model in 3D domains, and obtain three main results: the proof of an adequate Lojasiewicz-Simon inequality by using an abstract result; the rigorous proof (via a Galerkin ...
Artículo
An overview on numerical analyses of nematic liquid crystal flows
(Springer, 2011-09)
The purpose of this work is to provide an overview of the most recent numerical developments in the field of nematic liquid crystals. The Ericksen-Leslie equations govern the motion of a nematic liquid crystal. This system, ...