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On a Robust and Efficient Numerical Scheme for the Simulation of Stationary 3-Component Systems with Non-Negative Species-Concentration with an Application to the Cu Deposition from a Cu-(β-alanine)-Electrolyte

Materials and Surface Engineering Group, Institute of Materials Science and Engineering, Chemnitz University of Technology, D-09107 Chemnitz, Germany
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Academic Editor: Frank Werner
Received: 3 February 2021 / Revised: 25 March 2021 / Accepted: 26 March 2021 / Published: 30 March 2021
Three-component systems of diffusion–reaction equations play a central role in the modelling and simulation of chemical processes in engineering, electro-chemistry, physical chemistry, biology, population dynamics, etc. A major question in the simulation of three-component systems is how to guarantee non-negative species distributions in the model and how to calculate them effectively. Current numerical methods to enforce non-negative species distributions tend to be cost-intensive in terms of computation time and they are not robust for big rate constants of the considered reaction. In this article, a method, as a combination of homotopy methods, modern augmented Lagrangian methods, and adaptive FEMs is outlined to obtain a robust and efficient method to simulate diffusion–reaction models with non-negative concentrations. Although in this paper the convergence analysis is not described rigorously, multiple numerical examples as well as an application to elctro-deposition from an aqueous Cu2+-(β-alanine) electrolyte are presented. View Full-Text
Keywords: diffusion–reaction system; augmented lagrangian method; adaptive FEM; laminar diffusion boundary layer; three-component system; complexation of metal ions; obstacle problem diffusion–reaction system; augmented lagrangian method; adaptive FEM; laminar diffusion boundary layer; three-component system; complexation of metal ions; obstacle problem
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MDPI and ACS Style

Schwoebel, S.D.; Mehner, T.; Lampke, T. On a Robust and Efficient Numerical Scheme for the Simulation of Stationary 3-Component Systems with Non-Negative Species-Concentration with an Application to the Cu Deposition from a Cu-(β-alanine)-Electrolyte. Algorithms 2021, 14, 113. https://0-doi-org.brum.beds.ac.uk/10.3390/a14040113

AMA Style

Schwoebel SD, Mehner T, Lampke T. On a Robust and Efficient Numerical Scheme for the Simulation of Stationary 3-Component Systems with Non-Negative Species-Concentration with an Application to the Cu Deposition from a Cu-(β-alanine)-Electrolyte. Algorithms. 2021; 14(4):113. https://0-doi-org.brum.beds.ac.uk/10.3390/a14040113

Chicago/Turabian Style

Schwoebel, Stephan D., Thomas Mehner, and Thomas Lampke. 2021. "On a Robust and Efficient Numerical Scheme for the Simulation of Stationary 3-Component Systems with Non-Negative Species-Concentration with an Application to the Cu Deposition from a Cu-(β-alanine)-Electrolyte" Algorithms 14, no. 4: 113. https://0-doi-org.brum.beds.ac.uk/10.3390/a14040113

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