The Crank-Nicolson Extrapolation Stabilized Finite Element Method for Natural Convection Problem

Abstract EN

This paper studies a fully discrete Crank-Nicolson linear extrapolation stabilized finite element method for the natural convection problem, which is unconditionally stable and has second order temporal accuracy of O(Δt2+hΔt+hm).

A simple artificial viscosity stabilized of the linear system for the approximation of the new time level connected to antidiffusion of its effects at the old time level is used.

An unconditionally stability and an a priori error estimate are derived for the fully discrete scheme.

A series of numerical results are presented that validate our theoretical findings.