Numerical approximation of a concrete carbonation model: Study of the ‐law of propagation

Zurek, Antoine

doi:10.1002/num.22377

Cited by 10 publications

(12 citation statements)

References 12 publications

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“…Also, capturing numerically the large time behavior so that a certain power law is preserved requires a special care; compare e.g. the ideas from [6,19] to be adapted for the finite element method used here; see [17] for a detailed description of the numerical scheme used in this context. Of course, to bring the one-dimensional model equations to describe better the physical scenario of diffusants migrating into rubbers, more modeling components must be added, viz.…”

Section: Discussionmentioning

confidence: 99%

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A free boundary problem describing migration into rubbers -- quest of the large time behavior

Kumazaki¹,

Aiki²,

Muntean³

2021

Preprint

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In many industrial applications, rubber-based materials are routinely used in conjunction with various penetrants or diluents in gaseous or liquid form. It is of interest to estimate theoretically the penetration depth as well as the amount of diffusants stored inside the material. In this framework, we prove the global solvability and explore the large time-behavior of solutions to a one-phase free boundary problem with nonlinear kinetic condition that is able to describe the migration of diffusants into rubber. The key idea in the proof of the large time behavior is to benefit of a contradiction argument, since it is difficult to obtain uniform estimates for the growth rate of the free boundary due to the use of a Robin boundary condition posed at the fixed boundary.

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Section: Discussionmentioning

confidence: 99%

“…Finally, by integrating (4. 19) over [0, t] for t ∈ [0, T ] and using (A3), we see that u(t) ≤ b * /γ on [0, s(t)] for t ∈ [0, T ]. Thus, Lemma 4.2 is proven.…”

Section: Auxiliary Problemmentioning

confidence: 95%

A free boundary problem describing migration into rubbers -- quest of the large time behavior

Kumazaki¹,

Aiki²,

Muntean³

2021

Preprint

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“…Taking in (31) and (32) as test function ϕ = φ j for j ∈ {1, 2, • • • , N }, we obtain the following system of ordinary differential equations for…”

Section: Fixed-domain Transformation and Definition Of Weak Solutionsmentioning

confidence: 99%

“…e.g. [7,21,22,31]), large-time behavior of chemical species from the environment slowly penetrating by diffusion and swelling rubber-based materials (cf. e.g.…”

Section: Introductionmentioning

confidence: 99%

“…For instance, in [7], the authors show the convergence of a numerical scheme obtained by combining an Euler discretization in time with a Scharfetter-Gummel discretization in space for a concrete carbonation model with moving boundary reformulated for a fixed space domain. In [31], A. Zurek studies the long time regime of the moving interface driving the concrete carbonation reaction model by tailoring an implicit in time and finite volume in space scheme. He proves that the approximate free boundary increases in time with √ t-law as theoretically predicted in [3].…”

Section: Introductionmentioning

confidence: 99%

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Error estimates for semi-discrete finite element approximations for a moving boundary problem capturing the penetration of diffusants into rubber

Surendra¹,

Wondmagegne²,

Muntean³

2021

Preprint

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We study a semi-discrete finite element approximation of weak solutions to a moving boundary problem that models the diffusion of solvent into rubber. We report on both a priori and a posteriori error estimates for the mass concentration of the diffusants and respectively for the position of the moving boundary. Our working techniques include integral and energy-based estimates for a nonlinear parabolic problem posed in a transformed fixed domain combined with a suitable use of the interpolation-trace inequality to handle the interface terms. Numerical illustrations of our FEM approximations are within the experimental range and show good agreement with our theoretical investigation.

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A free boundary problem describing migration into rubbers – Quest for the large time behavior

2022

View full text Add to dashboard Cite

In many industrial applications, rubber‐based materials are routinely used in conjunction with various penetrants or diluents in gaseous or liquid form. It is of interest to estimate theoretically the penetration depth as well as the amount of diffusants stored inside the material. In this framework, we prove the global solvability and explore the large time‐behavior of solutions to a one‐phase free boundary problem with nonlinear kinetic condition that is able to describe the migration of diffusants into rubber. The key idea in the proof of the large time behavior is to benefit from a contradiction argument, since it is difficult to obtain uniform estimates for the growth rate of the free boundary due to the use of a Robin boundary condition posed at the fixed boundary.

show abstract

Numerical approximation of a concrete carbonation model: Study of the ‐law of propagation

Cited by 10 publications

References 12 publications

A free boundary problem describing migration into rubbers -- quest of the large time behavior

A free boundary problem describing migration into rubbers -- quest of the large time behavior

Error estimates for semi-discrete finite element approximations for a moving boundary problem capturing the penetration of diffusants into rubber

A free boundary problem describing migration into rubbers – Quest for the large time behavior

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