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On algebraically stabilized schemes for convection–diffusion–reaction problems

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Abstract

An abstract framework is developed that enables the analysis of algebraically stabilized discretizations in a unified way. This framework is applied to a discretization of this kind for convection–diffusion–reaction equations. The definition of this scheme contains a new limiter that improves a standard one in such a way that local and global discrete maximum principles are satisfied on arbitrary simplicial meshes.

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Authors and Affiliations

  1. Weierstrass Institute for Applied Analysis and Stochastics (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

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  1. Volker John
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Correspondence to Petr Knobloch.

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This work has been supported through the Grant No. 19-04243S of the Czech Science Foundation.

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John, V., Knobloch, P. On algebraically stabilized schemes for convection–diffusion–reaction problems. Numer. Math. 152, 553–585 (2022). https://doi.org/10.1007/s00211-022-01325-9

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