Skip to main content
SpringerLink
Log in

On implementation aspects of finite element method and its application

  • Published:
Advances in Computational Mathematics Aims and scope Submit manuscript

Abstract

This paper describes the usage of the finite element library CFEM for solution of boundary value problems for partial differential equations. The application of the finite element method is shown based on the weak formulation of a boundary value problem. A unified approach for solution of linear scalar, linear vector, and nonlinear vector problems is presented. A direct link between the mathematical formulation and the design of the computer code is shown. Several examples and results are shown.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. ALBERTA-FEM. http://www.alberta-fem.de/

  2. FEM4FSI/CFEM (Finite element method for fluid structure interactions - core library). http://marian.fsik.cvut.cz/svacek/cfem

  3. COMSOL multiphysics modeling software. www.comsol.com/

  4. deal.II (an open source finite element library). http://www.dealii.org/

  5. FEniCS Project. http://www.fenicsproject.org/

  6. Hermes (Hermes hp-FEM & hp-DG Library). http://hpfem.org/hermes

  7. libmesh library. http://libmesh.sourceforge.net/

  8. MFEM: Modular finite element methods library. mfem.org. https://doi.org/10.11578/dc.20171025.1248 https://doi.org/10.11578/dc.20171025.1248

  9. MSC Nastran (Multidisciplinary Structural Analysis). www.mscsoftware.com/product/msc-nastran

  10. OpenFOAM. The OpenFOAM Foundation. http://openfoam.org/

  11. Adams, R.A.: Sobolev Spaces. Academic Press, New York (1975)

    MATH  Google Scholar 

  12. Alns, M., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M., Wells, G.: The fenics project version 1.5. Arch. Numer. Softw 3(100) (2015)

  13. Armaly, B.F., Durst, F., Pereira, J.C.F., Schoenung, B.: Experimental and theoretical investigation of backward-facing step flow. J. Fluid Mech. 127, 473–496 (1983)

    Article  Google Scholar 

  14. Bangerth, W., Davydov, D., Heister, T., Heltai, L., Kanschat, G., Kronbichler, M., Maier, M., Turcksin, B., Wells, D.: The deal.ii library, version 8.4. J. Numer. Math. 24(3), 135–141 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  15. Brauer, J. (ed.): What Every Engineer Should Know about Finite Element Analysis, 2nd edn. Marcel Dekker Inc., New York (1993)

    Google Scholar 

  16. Ciarlet, P.G.: The Finite Element Methods for Elliptic Problems. North-Holland Publishing (1979)

  17. Donald, B.J.M.: Practical Stress Analysis with Finite Elements. Glasnevin Publishing, Dublin (2007)

    Google Scholar 

  18. Gajewski, H., Gröger, K., Zacharias, K.: Nichtlineare Operatorgleichungen und Operatordifferentialgleichungen. Springer, Berlin (1974)

    MATH  Google Scholar 

  19. Geuzaine, C., Remacle, J. -F.: GMSH: A three-dimensional finite element mesh generator with built-in pre- and post-processing facilities. Int. J. Numer. Methods Eng. 79(11), 1309–1331 (2009)

    Article  MATH  Google Scholar 

  20. Holub, A.I.: C+ C++: Programming with Objects in C and C++. McGraw-Hill Companies, New York (1991)

    Google Scholar 

  21. John, V., Matthies, G.: MooNMD - a program package based on mapped finite element methods. Comput. Vis. Sci. 6(2-3), 163–169 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  22. Koudelka, T., Krejcí, T., Kruis, J.: Moderate use of object oriented programming for scientific computing. In: Proceedings of the Seventh International Conference on Engineering Computational Technology. Paper 68. Civil-Comp Press, Stirlingshire (2010), https://doi.org/10.4203/ccp.94.68

  23. Kozel, K., Louda, P., Sváček, P., Příhoda, J.: Finite volume and finite element methods applied to backward facing step flows. In: 1st International Conference ”From Scientific Computing to Computational Engineering”, p. 10 pp. University of Patras, Patras. CD ROM Proceedings (2004)

  24. Schmidt, A., Siebert, K.G.: Design of Adaptive Finite Element Software. The Finite Element Toolbox ALBERTA. Springer, Berlin (2005)

    MATH  Google Scholar 

  25. Schreiner, A.: Object-Oriented Programming with ANSI-C (2011)

  26. Solin, P., Andrs, D., Cerveny, J., Simko, M.: Pde-independent adaptive hp-FEM based on hierarchic extension of finite element spaces. J. Comput. Appl. Math. 233, 3086–3094 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  27. Solin, P., Dubcova, L., Kruis, J.: Adaptive hp-FEM with dynamical meshes for transient heat and moisture transfer problems. J. Comput. Appl. Math. 233, 3103–3112 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  28. Sváček, P.: Finite element method application for turbulent and transitional flows. In: Proceedings of the Conference on Modelling Fluid Flow, p. 7 pp. Budapest University of Technology and Economics, Department of Fluid Mechanics, Budapest (2015). Art. no. 83

  29. Sváček, P.: On the finite element method application for approximation of free-surface flows with surface tension and contact angles. Appl. Mech. Mater. 821, 129–137 (2016)

    Article  Google Scholar 

  30. Sváček, P., Horáček, J.: On application of finite element method for approximation of 3d flow problems. In: Simurda, D., Bodnar T. (eds.) Topical Problems of Fluid Mechanics 2015, pp. 175–182 (2015)

  31. Sváček, P., Horáček, J.: On mathematical modeling of fluid–structure interactions with nonlinear effects: Finite element approximations of gust response. J. Comput. Appl. Math. 273(0), 394–403 (2015)

    MathSciNet  MATH  Google Scholar 

  32. Wilbrandt, U., Bartsch, C., Ahmed, N., Alia, N., Anker, F., Blank, L., Caiazzo, A., Ganesan, S., Giere, S., Matthies, G., Meesala, R., Shamim, A., Venkatesan, J., John, V.: ParMooN - A modernized program package based on mapped finite elements. Comput. Math. Appl. 74, 74–88 (2017)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

The authors acknowledge the support from the EU Operational Programme Research, Development and Education, and from the Center of Advanced Aerospace Technology (CZ.02.1.01/0.0/0.0/16_019/0000826), Faculty of Mechanical Engineering, Czech Technical University in Prague.

Author information

Authors and Affiliations

  1. Department of Technical Mathematics, Faculty of Mechanical Engineering, Center of Advanced Aerospace Technology, Czech Technical University in Prague, Technická 4, 166 01, Prague 6, Czech Republic

    Petr Sváček

Authors
  1. Petr Sváček
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Petr Sváček.

Additional information

Communicated by: Pavel Solin

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Sváček, P. On implementation aspects of finite element method and its application. Adv Comput Math 45, 2065–2081 (2019). https://doi.org/10.1007/s10444-019-09685-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10444-019-09685-x

Keywords

Mathematics Subject Classification (2010)

Search

Navigation