Local and Parallel Stabilized Finite Element Methods Based on the Lowest Equal-Order Elements for the Stokes–Darcy Model

Jing Han and Guangzhi Du ()
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Jing Han: School of Mathematics and Statistics, Shandong Normal University, Jinan 250014, China
Guangzhi Du: School of Mathematics and Statistics, Shandong Normal University, Jinan 250014, China

Mathematics, 2023, vol. 11, issue 23, 1-19

Abstract: In this article, two kinds of local and parallel stabilized finite element methods based upon two grid discretizations are proposed and investigated for the Stokes–Darcy model. The lowest equal-order finite element pairs ( P 1 - P 1 - P 1 ) are taken into account to approximate the velocity, pressure, and piezometric head, respectively. To circumvent the inf-sup condition, the stabilized term is chosen as the difference between a consistent and an under-integrated mass matrix. The proposed algorithms consist of approximating the low-frequency component on the global coarse grid and the high-frequency component on the local fine grid and assembling them to obtain the final approximation. To obtain a global continuous solution, the technique tool of the partition of unity is used. A rigorous theoretical analysis for the algorithms was conducted and numerical experiments were carried out to indicate the validity and efficiency of the algorithms.

Keywords: Stokes–Darcy model; stabilized finite element method; local and parallel finite element method; partition of unity (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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