A new stabilised finite element method for the Darcy-Forchheimer model

G.R. Barrenechea; M. González Taboada; F. Hecht; H. Varela

doi:10.1016/j.cam.2026.118137

A new stabilised finite element method for the Darcy-Forchheimer model

G.R. Barrenechea
, M. González Taboada^*
, F. Hecht
, H. Varela

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, we propose a new stabilised finite element method for the Darcy-Forchheimer model based on the jump stabilisation technique. We prove the well-posedness of the discrete scheme and develop an a priori error analysis. We provide two academic examples that support the theory and study the effect of the Forchheimer number on convergence. Finally, we adapt the method to solve the coupling of the Darcy-Forchheimer model with a heat equation and provide several numerical experiments, including an application to the simulation of wood drying and a three-dimensional example.

Original language	English
Article number	118137
Journal	Journal of Computational and Applied Mathematics
Volume	493
Early online date	19 Sept 2026
DOIs	https://doi.org/10.1016/j.cam.2026.118137
Publication status	E-pub ahead of print - 19 Sept 2026

Funding

M.G. and H.V. acknowledge support from the Spanish Ministerio de Ciencia e Innovación and Xunta de Galicia through grants PID2023-150390OB-I00 and Ayuda de Grupos de Referencia Competitiva ED431C 2022/47, respectively. H.V. also acknowledges support from the Spanish Ministerio de Educación through grant FPU18/06125. Funding for open access charge is acknowledged to Universidade da Coruña/CISUG.

Keywords

Darcy-Forchheimer
Stabilised finite element method
Divergence-free discrete velocity
65N30
65N12
65N15

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10.1016/j.cam.2026.118137Licence: CC BY-NC-ND 4.0

Barrenechea-etal-2026-A-new-stabilised-finite-element-method-for-the-Darcy-Forchheimer-modelFinal published version, 8.39 MBLicence: CC BY-NC-ND 4.0

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title = "A new stabilised finite element method for the Darcy-Forchheimer model",

abstract = "In this paper, we propose a new stabilised finite element method for the Darcy-Forchheimer model based on the jump stabilisation technique. We prove the well-posedness of the discrete scheme and develop an a priori error analysis. We provide two academic examples that support the theory and study the effect of the Forchheimer number on convergence. Finally, we adapt the method to solve the coupling of the Darcy-Forchheimer model with a heat equation and provide several numerical experiments, including an application to the simulation of wood drying and a three-dimensional example.",

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AU - Barrenechea, G.R.

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AU - Hecht, F.

AU - Varela, H.

PY - 2026/9/19

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AB - In this paper, we propose a new stabilised finite element method for the Darcy-Forchheimer model based on the jump stabilisation technique. We prove the well-posedness of the discrete scheme and develop an a priori error analysis. We provide two academic examples that support the theory and study the effect of the Forchheimer number on convergence. Finally, we adapt the method to solve the coupling of the Darcy-Forchheimer model with a heat equation and provide several numerical experiments, including an application to the simulation of wood drying and a three-dimensional example.

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KW - Stabilised finite element method

KW - Divergence-free discrete velocity

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KW - 65N12

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JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

M1 - 118137

ER -

A new stabilised finite element method for the Darcy-Forchheimer model

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