A combined stabilized mixed finite element and discontinuous Galerkin method for coupled Stokes and Darcy flows with transport. (15th August 2022)

• Record Type: Journal Article
• Authors: Song, Junpeng; Rui, Hongxing
• Is Part Of: Computers & mathematics with applications. Volume 120(2022)
• Page Start: 92
• Page End: 104
• Publication Date: 2022-08-15
• Subjects: Stokes-Darcy flows with transport -- Crouzeix-Raviart element -- Symmetric interior penalty Galerkin -- "Cut-off" -- Error estimates; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2022.06.023
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: This paper presents a combined stabilized mixed finite element and discontinuous Galerkin method for coupled Stokes-Darcy flows model with transport, where the fluid viscosity depends on the concentration. We use nonconforming piecewise linear Crouzeix-Raviart (C-R) element to approximate velocity, piecewise constant function to approximate pressure and the symmetric interior penalty Galerkin (SIPG) method to solve concentration equation. A "cut-off" operator is introduced into SIPG scheme to avoid the assumption on the boundness of infinity norms of approximate velocity in convergence analysis. Optimal a priori error estimates for the full discrete scheme are obtained. Finally, some numerical examples are presented to verify the theoretical analysis, and a water injection oil production process is simulated to illustrate the practicability of our method.