TITLE:
A Second Order Characteristic Mixed Finite Element Method for Convection Diffusion Reaction Equations
AUTHORS:
Tongjun Sun
KEYWORDS:
Mixed Finite Element Method, Characteristic Method, Second Order Accuracy, Convection Diffusion Reaction Equations
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.5 No.6,
June
27,
2017
ABSTRACT: A combined approximate scheme is defined for convection-diffusion-reaction equations. This scheme is constructed by two methods. Standard mixed finite element method is used for diffusion term. A second order characteristic finite element method is presented to handle the material derivative term, that is, the time derivative term plus the convection term. The stability is proved and the L2-norm error estimates are derived for both the scalar unknown variable and its flux. The scheme is of second order accuracy in time increment, symmetric, and unconditionally stable.