Approximation by an iterative method for regular solutions for incompressible fluids with mass diffusion

Guillén-González, Francisco; Damázio, Pedro D.; Rojas-Medar, Marko Antonio

doi:10.1016/j.jmaa.2006.03.009

Cited by 18 publications

(41 citation statements)

References 3 publications

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“…The first result is similar to one firstly presented in [9], with the difference that for the result stated here the regularity conditions on the coefficients of the starting inequality are slightly stronger. As consequence, we are able to improve the exponent of the resulting inequality, which is important for our final results.…”

Section: Some Technical Resultssupporting

confidence: 81%

“…As consequence, we are able to improve the exponent of the resulting inequality, which is important for our final results. The proof is similar to the one in [9], with suitable modifications; we do it here just for completeness.…”

Section: Some Technical Resultsmentioning

confidence: 88%

“…In fact, it was previously applied to a different fluid model (incompressible fluids with mass diffusion) in [9]. To prove the convergence of the sequence of approximate solutions, we use the same idea used in [9], that is, we prove that it is a Cauchy sequence in a suitable functional space.…”

Section: Introductionmentioning

confidence: 99%

“…To prove the convergence of the sequence of approximate solutions, we use the same idea used in [9], that is, we prove that it is a Cauchy sequence in a suitable functional space. We also should stress, however, that since the our fluid model is different from the one in [9], and one of the nonlinearities present in (1.1)-(1.2) is really hard since it is in the higher order operator, the estimates necessary to complete the argument are very hard to obtain.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

On an Iterative Method for Approximate Solutions of a Generalized Boussinesq Model

Boldrini

Climent-Ezquerra

Rojas-Medar

et al. 2009

J. Math. Fluid Mech.

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Abstract. An iterative method is proposed for finding approximate solutions of an initial and boundary value problem for a nonstationary generalized Boussinesq model for thermally driven convection of fluids with temperature dependent viscosity and thermal conductivity. Under certain conditions, it is proved that such approximate solutions converge to a solution of the original problem; moreover, convergence-rate bounds for the constructed approximate solutions are also obtained.

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Section: Some Technical Resultssupporting

confidence: 81%

Section: Some Technical Resultsmentioning

confidence: 88%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

On an Iterative Method for Approximate Solutions of a Generalized Boussinesq Model

Boldrini

Climent-Ezquerra

Rojas-Medar

et al. 2009

J. Math. Fluid Mech.

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show abstract

“…We complete these models with the following boundary conditions (9) u | Σ = 0, ∂ρ ∂n Σ = 0 (where n(x ) is the outwards unit normal vector on the boundary Γ) and initial conditions (10) ρ(x, 0) = ρ 0 (x), u(x, 0) = u 0 (x), x ∈ Ω.…”

Section: ) (ρU) T + ∇ · ((ρU − λ∇ρ) ⊗ U) = ρU T + ((ρU − λ∇ρ) · ∇)U mentioning

confidence: 99%

Unconditional stability and convergence of fully discrete schemes for $2D$ viscous fluids models with mass diffusion

Guillén-González

Gutiérrez-Santacreu²

2008

Math. Comp.

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Abstract. In this work we develop fully discrete (in time and space) numerical schemes for two-dimensional incompressible fluids with mass diffusion, also so-called Kazhikhov-Smagulov models. We propose at most H 1 -conformed finite elements (only globally continuous functions) to approximate all unknowns (velocity, pressure and density), although the limit density (solution of continuous problem) will have H 2 regularity. A backward Euler in time scheme is considered decoupling the computation of the density from the velocity and pressure.Unconditional stability of the schemes and convergence towards the (unique) global in time weak solution of the models is proved. Since a discrete maximum principle cannot be ensured, we must use a different interpolation inequality to obtain the strong estimates for the discrete density, from the used one in the continuous case. This inequality is a discrete version of the GagliardoNirenberg interpolation inequality in 2D domains. Moreover, the discrete density is truncated in some adequate terms of the velocity-pressure problem.

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Approximation by an iterative method of a low‐Mach model with temperature dependent viscosity

Calgaro

Colin

Creusé

et al. 2018

Math Methods in App Sciences

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In this work, we prove the existence and the uniqueness of the strong solution of a low‐Mach model, for which the dynamic viscosity of the fluid is a given function of its temperature. The method is based on the convergence study of a sequence towards the solution, for which the rates are also given. The originality of the approach is to consider the system in terms of the temperature and the velocity, leading to a nonlinear temperature equation and the development of some specific tools and results.

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Approximation by an iterative method for regular solutions for incompressible fluids with mass diffusion

Cited by 18 publications

References 3 publications

On an Iterative Method for Approximate Solutions of a Generalized Boussinesq Model

On an Iterative Method for Approximate Solutions of a Generalized Boussinesq Model

Unconditional stability and convergence of fully discrete schemes for $2D$ viscous fluids models with mass diffusion

Approximation by an iterative method of a low‐Mach model with temperature dependent viscosity

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