The Quadratic Discontinuous Finite Volume Element Schemes for Elliptic Problems
Abstract
The objective of the paper is to develop the quadratic discontinuous finite volume methods (DFVM) for solving elliptic equations with variable coefficients. The proposed numerical schemes are composed of the discontinuous Galerkin (DG) method with different interior penalty formulations (IIPG, NIPG, SIPG) and the finite volume element method which the trial function is discontinuous quadratic element function. Subsequently, with the specialized projection techniques, we built up a bridge between the bilinear form of DFVM and that of DG method, which simplifies the analysis and proves the optimal error estimate of the schemes in the broken $H^1$ norm. Finally, we provide numerical simulations to validate the theoretical findings.
Fields of Study & Subjects
Advanced Numerical Methods in Computational Mathematics
Computational Fluid Dynamics and Aerodynamics
Advanced Numerical Analysis Techniques
Publication details
- Journal / source
- Journal of Computational Mathematics
- Volume
- 44
- Issue
- 6
- Pages
- 1608–1630
- Publication date
- 4 March 2026
- Language
- EN