An algebraic flux correction scheme satisfying the discrete maximum principle and linearity preservation on general meshes

Abstract

This work is devoted to the proposal of a new flux limiter that makes the algebraic flux correction finite element scheme linearity and positivity preserving on general simplicial meshes. Minimal assumptions on the limiter are given in order to guarantee the validity of the discrete maximum principle, and then a precise definition of it is proposed and analyzed.

Numerical results for convection- diffusion problems confirm the theory.

Keywords

• Finite element method
• convection-diffusion equation
• algebraic flux correction
• discrete maximum principle
• linearity preservation