| 1. |
- Brunström, Mats, 1960-, et al.
(author)
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Computer-aided assessment based on dynamic mathematics investigations
- 2020
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In: Proceedings of the Tenth ERME Topic Conference (ETC 10) on Mathematics Education in the Digital Age (MEDA), 16-18 September 2020 in Linz, Austria. - Linz, Austria.
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Conference paper (peer-reviewed)abstract
- In the poster, we will present a planned study focusing on the design of DMS tasks and elaborated feedback within a CAA system. The study will be conducted in a first year engineering mathematics course during autumn 2020.
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| 2. |
- Brunström, Mats, 1960-, et al.
(author)
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Designing for a combined use of a dynamic mathematics software environment and a computer-aided assessment system
- 2022
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In: Proceedings of the Twelfth Congress of the European Research Society in Mathematics Education (CERME12). - : ERME.
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Conference paper (peer-reviewed)abstract
- This paper reports on a pilot study with the focus on (re)design of a digitized task environment utilizing two types of technology – a dynamic mathematics software and a computer-aided assessment system. The data consist of responses from 256 first year engineering students, taking their first Calculus course, on two different types of task. The results are discussed in relation to (re)design of tasks as well as possible feedback design options to enable a formative assessment approach.
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| 3. |
- Fahlgren, Maria, 1966-, et al.
(author)
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Designing tasks and feedback utilizing a combination of a dynamic mathematics software and a computer-aided assessment system
- 2022
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In: Proceedings of the 15th International Conference on Technology in Mathematics Teaching (ICTMT 15). - Aarhus : Danish School of Education, Aarhus Unviersity. - 9788775075256 ; , s. 272-279
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Conference paper (peer-reviewed)abstract
- This paper reports on the planning of a design-based research (DBR) study, where the main aim is to develop principles in designing technology-enhanced learning environment utilizing a combination of a dynamic mathematics software (DMS) and a computer-aided assessment (CAA) system. The focus is on the design of tasks and automated feedback of high quality so as to enhance first year engineering students’ engagement in and conceptual understanding of mathematical contents. The paper outlines the rationale for the project and highlights theoretical aspects that will be considered in the study. Moreover, some findings from a pilot study that will inform the first cycle of the DBR study are presented.
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| 4. |
- Nepal, Surendra, et al.
(author)
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A Moving Boundary approach of Capturing diffusants Penetration into Rubber : FEM Approximation and Comparison with laboratory Measurements
- 2021
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In: KGK Kautschuk, Gummi, Kunststoffe. - : Huethig GmbH & Co. KG. - 0948-3276. ; 74:5, s. 61-69
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Journal article (peer-reviewed)abstract
- To model the penetration of diffusants into dense and foamed rubbers a moving -boundary scenario is proposed. After a brief discussion of scaling arguments, we present a finite element approximation of the moving boundary problem. To overcome numerical difficulties due to the a priori unknown motion of the diffusants penetration front, we transform the governing model equations from the physical domain with moving unknown boundary to a fixed fictitious domain. We then solve the transformed equations by the finite element method and explore the robustness of our approximations with respect to relevant model parameters. Finally, we discuss numerical estimations of the expected large -time behavior of the material.
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| 5. |
- Nepal, Surendra, 1990-
(author)
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A moving boundary problem for capturing the penetration of diffusant concentration into rubbers : Modeling, simulation and analysis
- 2022
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Licentiate thesis (other academic/artistic)abstract
- We propose a moving-boundary scenario to model the penetration of diffusants into rubbers. Immobilizing the moving boundary by using the well-known Landau transformation transforms the original governing equations into new equations posed in a fixed domain. We solve the transformed equations by the finite element method and investigate the parameter space by exploring the eventual effects of the choice of parameters on the overall diffusants penetration process. Numerical simulation results show that the computed penetration depths of the diffusant concentration are within the range of experimental measurements. We discuss numerical estimations of the expected large-time behavior of the penetration fronts. To have trust in the obtained simulation results, we perform the numerical analysis for our setting. Initially, we study semi-discrete finite element approximations of the corresponding weak solutions. We prove both a priori and a posteriori error estimates for the mass concentration of the diffusants, and respectively, for the a priori unknown position of the moving boundary. Finally, we present a fully discrete scheme for the numerical approximation of model equations. Our scheme is based on the Galerkin finite element method for the space discretization combined with the backward Euler method for time discretization. In addition to proving the existence and uniqueness of a solution to the fully discrete problem, we also derive a priori error estimates for the mass concentration of the diffusants, and respectively, for the position of the moving boundary that fit to our implementation in Python. Our numerical illustrations verify the obtained theoretical order of convergence in physical parameter regimes.
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| 6. |
- Nepal, Surendra, et al.
(author)
-
Analysis of a fully discrete approximation to a moving-boundary problem describing rubber exposed to diffusants
- 2023
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In: Applied Mathematics and Computation. - : Elsevier. - 0096-3003 .- 1873-5649. ; 442
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Journal article (peer-reviewed)abstract
- We present a fully discrete scheme for the numerical approximation of a moving-boundary problem describing diffusants penetration into rubber. Our scheme utilizes the Galerkin finite element method for the space discretization combined with the backward Euler method for the time discretization. Besides dealing with the existence and uniqueness of solution to the fully discrete problem, we assume sufficient regularity for the solution to the target moving boundary problem and derive a a priori error estimates for the mass concentration of the diffusants, and respectively, for the position of the moving boundary. Our numerical results illustrate the obtained theoretical order of convergence in physical parameter regimes.
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| 7. |
- Nepal, Surendra, et al.
(author)
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Error estimates for semi-discrete finite element approximations for a moving boundary problem capturing the penetration of diffusants into rubber
- 2022
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In: International Journal of Numerical Analysis & Modeling. - : ISCI-INST SCIENTIFIC COMPUTING & INFORMATION. - 1705-5105. ; 19:1, s. 101-125
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Journal article (peer-reviewed)abstract
- We consider a moving boundary problem with kinetic condition that describes the diffusion of solvent into rubber and study semi-discrete finite element approximations of the corresponding weak solutions. We report on both a priori and a posteriori error estimates for the mass concentration of the diffusants, and respectively, for the a priori unknown 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. This work is a preliminary investigation necessary before extending the current moving boundary modeling to account explicitly for the mechanics of hyperelastic rods to capture a directional swelling of the underlying elastomer.
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| 8. |
- Nepal, Surendra, et al.
(author)
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Random walks and moving boundaries : Estimating the penetration of diffusants into dense rubbers
- 2023
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In: Probabilistic Engineering Mechanics. - : Elsevier. - 0266-8920 .- 1878-4275. ; 74
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Journal article (peer-reviewed)abstract
- For certain materials science scenarios arising in rubber technology, one-dimensional moving boundary problems with kinetic boundary conditions are capable of unveiling the large-time behavior of the diffusants penetration front, giving a direct estimate on the service life of the material. Driven by our interest in estimating how a finite number of diffusant molecules penetrate through a dense rubber, we propose a random walk algorithm to approximate numerically both the concentration profile and the location of the sharp penetration front. The proposed scheme decouples the target evolution system in two steps: (i) the ordinary differential equation corresponding to the evaluation of the speed of the moving boundary is solved via an explicit Euler method, and (ii) the associated diffusion problem is solved by a random walk method. To verify the correctness of our random walk algorithm we compare the resulting approximations to computational results based on a suitable finite element approach with a controlled convergence rate. Our numerical results recover well penetration depth measurements of a controlled experiment designed specifically for this setting.
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