Work

A Bound-Preserving and Conservative Enriched Galerkin Method for Elliptic Problems

Year: 2026

Type: article

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.

Source: SIAM Journal on Scientific Computing

DOI: 10.1137/25m1780493

Authors: Gabriel R. Barrenechea, Philip L. Lederer, Andreas Rupp

Institutions: University of Strathclyde, Universität Hamburg, Saarland University

Language: English

Topic: Advanced Numerical Methods in Computational Mathematics

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: green

Funders: Leverhulme Trust, Academy of Finland

Awards: Uncertainty quantification for PDEs on hypergraphs, G33094125, G4716734331, G7623643547, Flagship of Advanced Mathematics for Sensing, Imaging and Modelling