Interpolated Boundary Conditions in the Finite Element Method

This paper shows that the technique introduced in Berger, Scott and Strang 2 can achieve optimal accuracy if the approximating functions interpolate boundary conditions at the Lobatto quadrature points for each element edge on the boundary. No modification of the energy form is required. Estimates are derived in lower norms as well as in the energy norm. A numerical integration scheme is presented that yields optimal accuracy for piecewise quadratics.