A Bound-Preserving and Conservative Enriched Galerkin Method for Elliptic Problems
Abstract
Abstract. We propose a locally conservative enriched Galerkin scheme that preserves the physical bounds for an elliptic problem. To this end, we use a substantial overpenalization of the discrete solution’s jumps to obtain optimal convergence. To avoid the ill-conditioning issues that arise in overpenalized schemes, we introduce an involved splitting approach that separates the system of equations for the discontinuous solution part from the system of equations for the continuous solution part, yielding well-behaved subproblems. We prove the existence of discrete solutions and optimal error estimates, which are validated numerically.
Fields of Study & Subjects
Advanced Numerical Methods in Computational Mathematics
Numerical methods in engineering
Differential Equations and Numerical Methods
Publication details
- Journal / source
- SIAM Journal on Scientific Computing
- Volume
- 48
- Issue
- 3
- Pages
- A1761–A1784
- Publication date
- 17 June 2026
- Language
- EN