Abstract
The Hermite triangular element of degree three requires partial derivative values at the degrees of freedom. It can reconstruct polynomials of degree three on each element. In the case of problems subject to Dirichlet boundary conditions partial derivative values are not given on the boundary. We cannot, therefore, apply the element directly to those problems. Here we make variants of the Hermite element. Replacing the conventional Hermite elements by them near the boundary enables us to treat those problems easily. We apply this method to the Poisson problem to present the best possible a priori estimate and some numerical results.
