A Structure-Preserving Nonconforming FEM of Nonlinear Kirchhoff-Type Equation with Damping
Abstract
Superconvergent behavior for nonlinear Kirchhoff-type equations with damping is researched by a structure-preserving nonconforming finite element method (FEM). A new implicit energy dissipation scheme is developed and the numerical solution is bounded in energy norm. The existence of the numerical solution is obtained with the help of the Brouwer fixed-point theorem and then the uniqueness is derived. Superconvergence characteristics are revealed by virtue of the properties of nonconforming finite elements and a special splitting technique. Numerical tests confirm the correctness of the theoretical research results.
Fields of Study & Subjects
Advanced Numerical Methods in Computational Mathematics
Stability and Controllability of Differential Equations
Numerical methods for differential equations
Publication details
- Journal / source
- Journal of Computational Mathematics
- Volume
- 44
- Issue
- 5
- Pages
- 1248–1268
- Publication date
- 26 January 2026