Characteristic stabilized finite element method for non-stationary conduction-convection problems

Purpose: This paper aims to propose a characteristic stabilized finite element method for non-stationary conduction-convection problems. Design/methodology/approach: To avoid difficulty caused by the trilinear term, the authors use the characteristic method to deal with the time derivative term and the advection term. The space discretization adopts the low-order triples (i.e. P₁-P₁-P₁ and P₁-P₀-P₁ triples). As low-order triples do not satisfy inf-sup condition, the authors use the stability technique to overcome this flaw. Findings: The stability and the convergence analysis shows that the method is stable and has optimal-order error estimates. Originality/value: Numerical experiments confirm the theoretical analysis and illustrate that the authors’ method is highly effective and reliable, and consumes less CPU time.