A High-Order Mixed Finite Element Method for Second Order Elliptic Equations on Curved Domain with Boundary Value Corrections
Abstract
This paper presents a boundary corrections mixed finite element method for second order elliptic equations with the non-homogeneous Neumann boundary condition on curved domains. A key feature of the boundary value corrections is the shift from the true boundary to a surrogate boundary, which avoids numerical integration formula on curved elements. We consider the high-order Raviart-Thomas element $(RT_k)$ of degree $k ≥ 1$ on triangular meshes, achieving an $O(h^{k+1/2})$ convergence in the $L^2$-norm estimate for the velocity field and an $O(h^k)$ convergence in the $H^1$-norm estimate for the pressure. Finally, numerical experiments validate our theoretical results.
Fields of Study & Subjects
Advanced Numerical Methods in Computational Mathematics
Computational Fluid Dynamics and Aerodynamics
Matrix Theory and Algorithms
Publication details
- Journal / source
- International Journal of Numerical Analysis and Modeling
- Volume
- 23
- Issue
- 3
- Pages
- 442–459
- Publication date
- 11 March 2026
- Language
- EN