Preserving nonnegativity of an affine finite element approximation for a convection–diffusion–reaction problem

作者：

Highlights：

• We present a monotone FEM scheme for a convection–diffusion–reaction problem in 2, 3D.

• The considered equation does not possess an underlying maximum principle.

• Sufficient conditions are given to ensure the nonnegativity of the approximations.

• Numerical examples confirm the necessity and sufficiency of the conditions.

摘要

•We present a monotone FEM scheme for a convection–diffusion–reaction problem in 2, 3D.•The considered equation does not possess an underlying maximum principle.•Sufficient conditions are given to ensure the nonnegativity of the approximations.•Numerical examples confirm the necessity and sufficiency of the conditions.

论文关键词：65M60,35K57,35B09,Finite element method,Convection–diffusion–reaction,Nonnegativity,Boundedness

论文评审过程：Received 15 May 2015, Revised 10 February 2016, Available online 23 April 2016, Version of Record 19 May 2016.

论文官网地址：https://doi.org/10.1016/j.cam.2016.04.018