A high-order combined interpolation/finite element technique for evolutionary coupled groundwater-surface water problem
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_ | 1866915307046567936 |
|---|---|
| author | Ngondiep, Eric Binsultan, Areej A. Aldawish, Ibtisam M. |
| author_facet | Ngondiep, Eric Binsultan, Areej A. Aldawish, Ibtisam M. |
| contents | A high-order combined interpolation/finite element technique is developed for solving the coupled groundwater-surface water system that governs flows in karst aquifers. In the proposed high-order scheme we approximate the time derivative with piecewise polynomial interpolation of second-order and use the finite element discretization of piecewise polynomials of degree $d$ and $d+1$, where $d \geq 2$ is an integer, to approximate the space derivatives. The stability together with the error estimates of the constructed technique are established in $L^{\infty}(0,T;\text{\,}L^{2})$-norm. The analysis suggests that the developed computational technique is unconditionally stable, temporal second-order accurate and convergence in space of order $d+1$. Furthermore, the new approach is faster and more efficient than a broad range of numerical methods discussed in the literature for the given initial-boundary value problem. Some examples are carried out to confirm the theoretical results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_00707 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A high-order combined interpolation/finite element technique for evolutionary coupled groundwater-surface water problem Ngondiep, Eric Binsultan, Areej A. Aldawish, Ibtisam M. Numerical Analysis 65M10, 65M05 A high-order combined interpolation/finite element technique is developed for solving the coupled groundwater-surface water system that governs flows in karst aquifers. In the proposed high-order scheme we approximate the time derivative with piecewise polynomial interpolation of second-order and use the finite element discretization of piecewise polynomials of degree $d$ and $d+1$, where $d \geq 2$ is an integer, to approximate the space derivatives. The stability together with the error estimates of the constructed technique are established in $L^{\infty}(0,T;\text{\,}L^{2})$-norm. The analysis suggests that the developed computational technique is unconditionally stable, temporal second-order accurate and convergence in space of order $d+1$. Furthermore, the new approach is faster and more efficient than a broad range of numerical methods discussed in the literature for the given initial-boundary value problem. Some examples are carried out to confirm the theoretical results. |
| title | A high-order combined interpolation/finite element technique for evolutionary coupled groundwater-surface water problem |
| topic | Numerical Analysis 65M10, 65M05 |
| url | https://arxiv.org/abs/2505.00707 |