Numerical analysis of heat and moisture transport with a finite difference method

In this article, we study a system of nonlinear parabolic partial differential equations arising from the heat and moisture transport through textile materials with phase change. A splitting finite difference method with semi-implicit Euler scheme in time direction is proposed for solving the system of equations. We prove the existence and uniqueness of a classical positive solution to the parabolic system as well as the existence and uniqueness of a positive solution to the splitting finite difference system. We provide optimal error estimates for the splitting finite difference system under the condition that the mesh size and time step size are smaller than a positive constant which solely depends upon the physical parameters involved. Numerical results are presented to confirm our theoretical analysis. Numer Methods Partial Differential Eq 2013