On algebraically stabilized schemes for convection-diffusion-reaction problems

11/16/2021

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by   Volker John, et al.

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Weierstrass Institute

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Charles University in Prague

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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.