A Bound-Preserving and Conservative Enriched Galerkin Method for Elliptic Problems.
Saved in:
| Title: | A Bound-Preserving and Conservative Enriched Galerkin Method for Elliptic Problems. |
|---|---|
| Authors: | Barrenechea, Gabriel R.1 (AUTHOR) gabriel.barrenechea@strath.ac.uk, Lederer, Philip L.2 (AUTHOR) philip.lederer@uni-hamburg.de, Rupp, Andreas3 (AUTHOR) andreas.rupp@uni-saarland.de |
| Source: | SIAM Journal on Scientific Computing. 2026, Vol. 48 Issue 3, pA1761-A1784. 24p. |
| Subjects: | Galerkin methods, Elliptic equations, Finite element method, Approximation error, Numerical analysis, Mathematical regularization |
| 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. [ABSTRACT FROM AUTHOR] |
| Copyright of SIAM Journal on Scientific Computing is the property of Society for Industrial & Applied Mathematics and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Text: Availability: 0 |
|---|---|
| Header | DbId: egs DbLabel: Engineering Source An: 195222029 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
| IllustrationInfo | |
| Items | – Name: Title Label: Title Group: Ti Data: A Bound-Preserving and Conservative Enriched Galerkin Method for Elliptic Problems. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Barrenechea%2C+Gabriel+R%2E%22">Barrenechea, Gabriel R.</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> gabriel.barrenechea@strath.ac.uk</i><br /><searchLink fieldCode="AR" term="%22Lederer%2C+Philip+L%2E%22">Lederer, Philip L.</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> philip.lederer@uni-hamburg.de</i><br /><searchLink fieldCode="AR" term="%22Rupp%2C+Andreas%22">Rupp, Andreas</searchLink><relatesTo>3</relatesTo> (AUTHOR)<i> andreas.rupp@uni-saarland.de</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22SIAM+Journal+on+Scientific+Computing%22">SIAM Journal on Scientific Computing</searchLink>. 2026, Vol. 48 Issue 3, pA1761-A1784. 24p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Galerkin+methods%22">Galerkin methods</searchLink><br /><searchLink fieldCode="DE" term="%22Elliptic+equations%22">Elliptic equations</searchLink><br /><searchLink fieldCode="DE" term="%22Finite+element+method%22">Finite element method</searchLink><br /><searchLink fieldCode="DE" term="%22Approximation+error%22">Approximation error</searchLink><br /><searchLink fieldCode="DE" term="%22Numerical+analysis%22">Numerical analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+regularization%22">Mathematical regularization</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: 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. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of SIAM Journal on Scientific Computing is the property of Society for Industrial & Applied Mathematics and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
| PLink | https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=egs&AN=195222029 |
| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1137/25M1780493 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 24 StartPage: A1761 Subjects: – SubjectFull: Galerkin methods Type: general – SubjectFull: Elliptic equations Type: general – SubjectFull: Finite element method Type: general – SubjectFull: Approximation error Type: general – SubjectFull: Numerical analysis Type: general – SubjectFull: Mathematical regularization Type: general Titles: – TitleFull: A Bound-Preserving and Conservative Enriched Galerkin Method for Elliptic Problems. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Barrenechea, Gabriel R. – PersonEntity: Name: NameFull: Lederer, Philip L. – PersonEntity: Name: NameFull: Rupp, Andreas IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 05 Text: 2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 10648275 Numbering: – Type: volume Value: 48 – Type: issue Value: 3 Titles: – TitleFull: SIAM Journal on Scientific Computing Type: main |
| ResultId | 1 |
