A new algebraically stabilized method for convection-diffusion-reaction equations

Abstrakt

This paper is devoted to algebraically stabilized finite element methods for the numerical solution of convection-diffusion-reaction equations. First, the algebraic flux correction scheme with the popular Kuzmin limiter is presented.

This limiter has several favourable properties but does not guarantee the validity of the discrete maximum principle for non-Delaunay meshes. Therefore, a generalization of the algebraic flux correction scheme and a modification of the limiter are proposed which lead to the discrete maximum principle for arbitrary meshes.

Numerical results demonstrate the advantages of the new method.

Klíčová slova

• algebraic stabilization
• convection-diffusion-reaction equation
• Kuzmin limiter
• discrete maximum principle