The boundary penalty method for the diffusion equation subject to the specification of mass (Q876657)

A new boundary penalty finite element method for the one-dimensional time-dependent diffusion equation subject to the specification of mass is presented. Instead of solving the diffusion equation directly, a finite element method is used to solve a boundary penalty problem which is derived from the diffusion equation and analyse the error estimate of the semi-discrete approximations when the penalty parameter \(\epsilon\) is sufficiently small. The numerical experiments show that the method is very effective.