The Application of a Special Hermite Finite Element Coupled with Collocation to the Diffusion Equation

Abstract

In the paper, we propose an efficient method based on the use of a bicubic Hermite finite element coupled with collocation for the diffusion equation. This enables one to reduce the dimension of the system of equations in comparison with the standard finite element scheme. Numerical experiments confirm a theoretical convergence estimate and demonstrate the advantage of the proposed method.