This paper presents a $C^1$-conforming finite element method (FEM) for solving fourth-order ordinary differential equations (ODEs) using cubic Hermite basis functions. The proposed scheme inherently enforces $C^1$-continuity and accommodates both clamped and simply supported boundary conditions. A rigorous theoretical analysis demonstrates the method's stability and optimal convergence rates, achieving $\mathcal{O}(h^2)$ in the $H^2$-norm and $\mathcal{O}(h^4)$ in the $L^2$-norm. Numerical experiments validate the theoretical results, showing excellent agreement with exact solutions. The study underscores the efficacy of Hermite FEM for high-order BVPs, providing a robust and accurate computational framework.
Lubo, G. T. (2026). C1--Conforming Finite Element Method for Fourth-Order Ordinary Differential Equations. Computational Methods for Differential Equations, (), -. doi: 10.22034/cmde.2026.68585.3326
MLA
Lubo, G. T. . "C1--Conforming Finite Element Method for Fourth-Order Ordinary Differential Equations", Computational Methods for Differential Equations, , , 2026, -. doi: 10.22034/cmde.2026.68585.3326
HARVARD
Lubo, G. T. (2026). 'C1--Conforming Finite Element Method for Fourth-Order Ordinary Differential Equations', Computational Methods for Differential Equations, (), pp. -. doi: 10.22034/cmde.2026.68585.3326
CHICAGO
G. T. Lubo, "C1--Conforming Finite Element Method for Fourth-Order Ordinary Differential Equations," Computational Methods for Differential Equations, (2026): -, doi: 10.22034/cmde.2026.68585.3326
VANCOUVER
Lubo, G. T. C1--Conforming Finite Element Method for Fourth-Order Ordinary Differential Equations. Computational Methods for Differential Equations, 2026; (): -. doi: 10.22034/cmde.2026.68585.3326
)