| Issue |
ESAIM: M2AN
Volume 59, Number 5, September-October 2025
|
|
|---|---|---|
| Page(s) | 2763 - 2788 | |
| DOI | https://doi.org/10.1051/m2an/2025074 | |
| Published online | 15 October 2025 | |
HDG Methods for incompressible and immiscible two-phase flow in porous media: the existence and convergence of discrete solutions
1
School of Mathematic and Information Sciences, Guangzhou University, Guangzhou 510006, Guangdong, P.R. China
2
School of Mathematical Sciences and Fujian Provincial Key Laboratory on Mathematical Modeling and High Performance Scientific Computing, Xiamen University, Fujian 361005, P.R. China
* Corresponding author: chx@xmu.edu.cn
Received:
9
February
2025
Accepted:
4
September
2025
In this paper, we investigate the numerical approximation of incompressible, immiscible two-phase flow in porous media using backward Euler methods for time discretization and hybridized discontinuous Galerkin (HDG) methods for saturation and pressure discretizations. Using the Brouwer fixed-point theorem, we establish the existence of a discrete solution for the proposed scheme. Furthermore, the sequence of discrete solutions solved by the discrete scheme converges, potentially after passing to a subsequence, to a weak solution of the continuous problem. Finally, two numerical examples are presented to validate both the accuracy and performance of the discrete scheme.
Mathematics Subject Classification: 35K55 / 65M60 / 76S05 / 76T10
Key words: HDG methods / two-phase flow / existence of discrete solutions / stability / convergence
© The authors. Published by EDP Sciences, SMAI 2025
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