On algebraically stabilized schemes for convection-diffusion-reaction problems

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.

Keywords

• algebraic stabilization
• convection-diffusion problems
• finite element method
• discrete maximum principle