Title

Decoupled Characteristic Stabilized Finite Element Method for Time‐dependent Navier–Stokes/Darcy Model

Document Type

Article

Publication Date

7-16-2018

Publication Title

Numerical Methods for Partial Differential Equations

Volume

35

Issue

1

First page number:

267

Last page number:

294

Abstract

In this article, we propose and analyze a new decoupled characteristic stabilized finite element method for the time‐dependent Navier–Stokes/Darcy model. The key idea lies in combining the characteristic method with the stabilized finite element method to solve the decoupled model by using the lowest‐order conforming finite element space. In this method, the original model is divided into two parts: one is the nonstationary Navier–Stokes equation, and the other one is the Darcy equation. To deal with the difficulty caused by the trilinear term with nonzero boundary condition, we use the characteristic method. Furthermore, as the lowest‐order finite element pair do not satisfy LBB (Ladyzhen‐Skaya‐Brezzi‐Babuska) condition, we adopt the stabilized technique to overcome this flaw. The stability of the numerical method is first proved, and the optimal error estimates are established. Finally, extensive numerical results are provided to justify the theoretical analysis.

Keywords

Characteristic stabilized finite element method; Error estimate; Navier-Stokes/Darcy model

Disciplines

Applied Mathematics

Language

English

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