A Novel Implementation of Hermite Finite Element Methods in the deal.II Library
Abstract
A high-order finite element method based on Hermite interpolation polynomials is described and a software implementation in the deal.II finite element library ( https://dealii.org ) is proposed. This method can be used to strongly enforce continuity of spatial derivatives as well as solution value over element boundaries, which is necessary for solving fourth order partial differential equations (PDEs) in primal form and useful for some second order PDEs. The implementation is verified by solving the wave equation based on a modification of the PDE with a Lax–Wendroff-like procedure, allowing a high-order solution method with negligible additional computing time.
Fields of Study & Subjects
Numerical methods in engineering
Advanced Numerical Methods in Computational Mathematics
Numerical methods for differential equations
Publication details
- Journal / source
- ACM Transactions on Mathematical Software
- Publisher
- Association for Computing Machinery (ACM)
- Volume
- 52
- Issue
- 1
- Pages
- 1–31
- Publication date
- 16 February 2026
- Language
- EN