On algebraically stabilized schemes for convection-diffusion-reaction problems
Volker John, Petr Knobloch
TL;DR
This paper introduces a unified abstract framework for analyzing algebraically stabilized discretizations of convection-diffusion-reaction equations, featuring a new limiter that ensures maximum principles on arbitrary meshes.
Contribution
It develops a novel abstract framework and a new limiter for stabilized schemes, guaranteeing maximum principles on arbitrary simplicial meshes.
Findings
The framework enables unified analysis of algebraically stabilized schemes.
The new limiter improves standard methods to satisfy maximum principles.
The scheme is applicable to convection-diffusion-reaction problems on arbitrary meshes.
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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Taxonomy
TopicsNumerical methods for differential equations · Advanced Numerical Methods in Computational Mathematics · Computational Fluid Dynamics and Aerodynamics