On the numerical determination of eigenvalues/eigenvectors using a high regularity finite element method

This study investigates the numerical prediction of eigenvalues/eigenvectors in heat conduction transfer problems based on approximation spaces constructed using a high regularity Hermite finite element method (H-FEM). Special attention is given to the number of reliable numerical eigenvalues that can be estimated using this approach. The shape functions are constructed on quadrilateral elements by the tensor product of the generalization of Hermite functions in one-dimensional space. The numerical results obtained for selected eigenvalue/eigenvector problems using the H-FEM are compared with available analytical solutions and numerical solutions obtained using the high-order Lagrange FEM, as well as with the B-splines FEM. The numerical results demonstrate the superior accuracy of the H-FEM in predicting high order modes, thereby reducing the appearance of spurious branches in the spectrum.