Error control for the FEM approximation of an upscaled thermo-diffusion system with Smoluchowski interactions

O. Krehel, A. Muntean

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Abstract

We analyze a coupled system of evolution equations that describes the effect of thermal gradients on the motion and deposition of N populations of colloidal species diffusing and interacting together through Smoluchowski production terms. This class of systems is particularly useful in studying drug delivery, contaminant transport in complex media, as well as heat shocks thorough permeable media. The particularity lies in the modeling of the nonlinear and nonlocal coupling between diffusion and thermal conduction. We investigate the semidiscrete as well as the fully discrete a priori error analysis of the finite elements approximation of the weak solution to a thermo-diffusion reaction system posed in a macroscopic domain. The mathematical techniques include energy-like estimates and compactness arguments. Keywords: Thermo-diffusion, Soret and Dufour effects, colloids, Smoluchowski interactions, finite element approximation, convergence analysis, a priori error control.
Original languageEnglish
Place of PublicationEindhoven
PublisherTechnische Universiteit Eindhoven
Number of pages22
Publication statusPublished - 2014

Publication series

NameCASA-report
Volume1419
ISSN (Print)0926-4507

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