Hermite Finite Element Method for One-Dimensional Fourth-Order Boundary Value Problems.

One-dimensional fourth-order boundary value problems (BVPs) play a critical role in engineering applications, particularly in the analysis of beams. Current numerical investigations primarily concentrate on homogeneous boundary conditions. In addition to its high precision advantages, the Hermite finite element method (HFEM) is capable of directly computing both the function value and its derivatives. In this paper, both the cubic and quintic HFEM are employed to address two prevalent non-homogeneous fourth-order BVPs. Furthermore, a priori error estimations are established for both BVPs, demonstrating the optimal error convergence order in H 2 semi-norm and L 2 norm. Finally, a numerical simulation is presented to validate the theoretical results. [ABSTRACT FROM AUTHOR]