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Finite elements for scalar convection-dominated equations and incompressible flow problems: a never ending story?

  • Special Issue FEM Symposium 2017
  • Published:
Computing and Visualization in Science

Abstract

The contents of this paper is twofold. First, important recent results concerning finite element methods for convection-dominated problems and incompressible flow problems are described that illustrate the activities in these topics. Second, a number of, in our opinion, important open problems in these fields are discussed. The exposition concentrates on \(H^1\)-conforming finite elements.

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Acknowledgements

The work of P. Knobloch was supported through the Grant No. 16-03230S of the Czech Science Foundation. The work of J. Novo was supported by Spanish MINECO under Grants MTM2013-42538-P (MINECO, ES) and MTM2016-78995-P (AEI/FEDER, UE). We would like to thank an anonymous referee whose suggestions helped us to improve this paper.

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Authors and Affiliations

  1. Weierstrass Institute for Applied Analysis and Stochastics, Leibniz Institute in Forschungsverbund Berlin e. V. (WIAS), Mohrenstr. 39, 10117, Berlin, Germany

    Volker John

  2. Department of Mathematics and Computer Science, Freie Universität Berlin, Arnimallee 6, 14195, Berlin, Germany

    Volker John

  3. Department of Numerical Mathematics, Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 18675, Praha 8, Czech Republic

    Petr Knobloch

  4. Departamento de Matemáticas, Universidad Autónoma de Madrid, Madrid, Spain

    Julia Novo

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  1. Volker John
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Correspondence to Volker John.

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Communicated by Thomas Apel.

This paper is dedicated to Ulrich Langer and Arnd Meyer on the occasions of their 65th birthdays.

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John, V., Knobloch, P. & Novo, J. Finite elements for scalar convection-dominated equations and incompressible flow problems: a never ending story?. Comput. Visual Sci. 19, 47–63 (2018). https://doi.org/10.1007/s00791-018-0290-5

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