Stability analysis and energy-preserved schemes for coupled diffusion equations with interface conditions

Purpose The purpose of this study is to compare various approximations method such as finite element, finite volume and finite difference approximations for the coupled diffusion problem with interface conditions. The property of discrete energy conservation and stability analysis are the main contribution of this work for coupling problem. Two basic couplings (Dirichlet-Neumann and heat flux coupling) are considered along with the coupled diffusion equations. Design/methodology/approach The Crank–Nicolson scheme of finite volume, finite element and finite difference methods are used. Findings The authors show that conservation is preserved in the case of DN-coupling with one-sided approximation in both finite difference and finite volume schemes. However, heat flux is maintained the conservation by the central difference approximations along coupled diffusion equations. Originality/value This is the authors’ original work and modification of the previously published work mentioned in the paper.