A new conservative method for the unsteady heat equation

A new conservative finite difference scheme for the unsteady heat equation is proposed. The new numerical scheme is a simplified version of mimetic methods, it satisfies a discrete version of Green’s theorem, and it does not use ghost points at any stage of its development. Its formulation will be presented in terms of a simple matricial form, which covers the full range of time evaluations. This feature allows us to present a complete and elegant convergence analysis. Its precision is quadratic at the boundary so an overall higher order convergence rate, compared with finite difference methods, is achieved in space. Numerical tests show the advantage of the new scheme when its linear systems are solved by iterative Krylov methods.