A bound-preserving and conservative enriched Galerkin method for elliptic problems
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912772168613888 |
|---|---|
| author | Barrenechea, Gabriel R. Lederer, Philip L. Rupp, Andreas |
| author_facet | Barrenechea, Gabriel R. Lederer, Philip L. Rupp, Andreas |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_12338 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A bound-preserving and conservative enriched Galerkin method for elliptic problems Barrenechea, Gabriel R. Lederer, Philip L. Rupp, Andreas Numerical Analysis 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. |
| title | A bound-preserving and conservative enriched Galerkin method for elliptic problems |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2507.12338 |