A bound-preserving and conservative enriched Galerkin method for elliptic problems

Tools

Barrenechea, Gabriel R. and Lederer, Philip L and Rupp, Andreas (2026) A bound-preserving and conservative enriched Galerkin method for elliptic problems. SIAM Journal on Scientific Computing. ISSN 1064-8275 (In Press)

[thumbnail of Barrenechea-etal-SIAM-JSC-2026-A-bound-preserving-and-conservative-enriched-Galerkin-method] Text. Filename: Barrenechea-etal-SIAM-JSC-2026-A-bound-preserving-and-conservative-enriched-Galerkin-method.pdf
Accepted Author Manuscript
Restricted to Repository staff only until 1 January 2099.
Download (1MB) | Request a copy

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 over-penalization of the discrete solution’s jumps to obtain optimal convergence. To avoid the ill-conditioning issues that arise in over-penalized 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.

ORCID iDs

Barrenechea, Gabriel R. ORCID logoORCID: https://orcid.org/0000-0003-4490-678X, Lederer, Philip L and Rupp, Andreas;
CORE (COnnecting REpositories)