The boundary penalty method for the diffusion equation subject to the specification of mass

In this paper, we concern with a new boundary penalty finite element method for the one-dimensional time-dependent diffusion equation subject to the specification of mass. Instead of solving the diffusion equation directly, we will use the finite element method to solve a boundary penalty problem which is derived from the diffusion equation and analyse the error estimate of the semi-discrete and fully discrete approximations when the penalty parameter ε is sufficiently small. The numerical experiments show that our method is very effective and supports our analysis.