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Finite Element Methods for Parabolic Problems with Time-Dependent Domains: Application to a Milling Simulation

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Numerical Mathematics and Advanced Applications ENUMATH 2017 (ENUMATH 2017)

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 126))

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Abstract

We consider the finite element discretization of PDEs on time-dependent domains. Approximation of boundary conditions is one of the crucial aspects, as well as an appropriate approach to adaptive mesh refinement. We present some numerical test results and the application to the thermomechanical simulation of a milling process, where the domain changes in time due to material removal.

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Acknowledgements

The authors gratefully acknowledge the financial support by the German Research Foundation (DFG) via the project “Thermomechanical Deformation of Complex Workpieces in Drilling and Milling Processes” (MA1657/21-3) within the DFG Priority Program 1480 “Modeling, Simulation and Compensation of Thermal Effects for Complex Machining Processes”. Furthermore, we thank our project partners from ZeTeM Bremen and IFW Hannover for cooperation.

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Authors and Affiliations

  1. University of Bremen, Center for Industrial Mathematics (ZeTeM), Bremen, Germany

    Carsten Niebuhr & Alfred Schmidt

  2. MAPEX Center for Materials and Processes, Bremen, Germany

    Carsten Niebuhr & Alfred Schmidt

Authors
  1. Carsten Niebuhr
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  2. Alfred Schmidt
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Corresponding author

Correspondence to Alfred Schmidt .

Editor information

Editors and Affiliations

  1. University of Bergen, Bergen, Norway

    Florin Adrian Radu

  2. University of Bergen, Bergen, Norway

    Kundan Kumar

  3. University of Bergen, Bergen, Norway

    Inga Berre

  4. University of Bergen, Bergen, Norway

    Jan Martin Nordbotten

  5. Hasselt University, Diepenbeek, Belgium

    Iuliu Sorin Pop

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Niebuhr, C., Schmidt, A. (2019). Finite Element Methods for Parabolic Problems with Time-Dependent Domains: Application to a Milling Simulation. In: Radu, F., Kumar, K., Berre, I., Nordbotten, J., Pop, I. (eds) Numerical Mathematics and Advanced Applications ENUMATH 2017. ENUMATH 2017. Lecture Notes in Computational Science and Engineering, vol 126. Springer, Cham. https://doi.org/10.1007/978-3-319-96415-7_43

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