A Decoupling Method with Different Subdomain Time Steps for the Non-Stationary Navier-Stokes ⁄ Darcy Model

Pei-lin, Shi; Li, Kaitai; Jia, H. M.; Jia, Hongwei

doi:10.4208/jcm.1606-m2015-0436

Cited by 7 publications

(6 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Here h denotes the mesh size. To solve our problem, we use the following finite element subspace W h = H fh × H ph ⊂ W and Q h ⊂ Q :

\begin{array}{l} H_{fh} = ({};,, v_{h} \in H_{f} \cap C^{0} {(\overset{Ω}{true})}^{d}, v_{h} ∣_{K} \in P_{1} {(K)}^{d}, \forall K \in τ_{h}), \\ H_{ph} = ({};,, ψ_{h} \in H_{p} \cap C^{0} ((), \overset{true‾}{normalΩ}), ψ_{h} ∣_{K} \in P_{1} ((), K), \forall K \in τ_{h}), \\ Q_{h} = ({};,, q_{h} \in Q \cap C^{0} ((), \overset{true‾}{normalΩ}), q_{h} ∣_{K} \in P_{1} ((), K), \forall K \in τ_{h}) . \end{array}

…”

Section: The Decoupled Stabilized Characteristic Finite Element Methodsmentioning

confidence: 99%

“…Here h denotes the mesh size. To solve our problem, we use the following finite element subspace W h = H fh × H ph ⊂ W and Q h ⊂ Q [11]:…”

Section: The Decoupled Stabilized Characteristic Finite Element Methodsmentioning

confidence: 99%

“…In this section, we will derive the error estimate of the CSFEM. First, we assume that the solution ( u , p , ϕ ) of problems – satisfies the following regularity hypotheses :

\begin{array}{l} ((), 1) boldu \in L^{\infty} ((),,, 0, T, H^{2} {(Ω_{f})}^{2}), ϕ \in L^{\infty} ((),,, 0, T, H^{2} ((), {normalΩ}_{p})), \\ ((), 2) u_{t} \in L^{2} ((),,, 0, T, H^{2} {(Ω_{f})}^{2}), ϕ_{t} \in L^{2} ((),,, 0, T, H^{2} ((), {normalΩ}_{p})), \\ ((), 3) p \in L^{\infty} ((),,, 0, T, H^{1} ((), {normalΩ}_{f})), p_{t} \in L^{2} ((),,, 0, T, H^{1} ((), {normalΩ}_{f})) . \end{array}

…”

Section: The Error Analysismentioning

confidence: 99%

“…In this section, we will derive the error estimate of the CSFEM. First, we assume that the solution (u, p, ) of problems (2.1)-(2.6) satisfies the following regularity hypotheses [11]:…”

Section: The Error Analysismentioning

confidence: 99%

See 3 more Smart Citations

Decoupled characteristic stabilized finite element method for time‐dependent Navier–Stokes/Darcy model

Jia

2018

Numerical Methods Partial

View full text Add to dashboard Cite

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.

show abstract

“…Here h denotes the mesh size. To solve our problem, we use the following finite element subspace W h = H fh × H ph ⊂ W and Q h ⊂ Q :

\begin{array}{l} H_{fh} = ({};,, v_{h} \in H_{f} \cap C^{0} {(\overset{Ω}{true})}^{d}, v_{h} ∣_{K} \in P_{1} {(K)}^{d}, \forall K \in τ_{h}), \\ H_{ph} = ({};,, ψ_{h} \in H_{p} \cap C^{0} ((), \overset{true‾}{normalΩ}), ψ_{h} ∣_{K} \in P_{1} ((), K), \forall K \in τ_{h}), \\ Q_{h} = ({};,, q_{h} \in Q \cap C^{0} ((), \overset{true‾}{normalΩ}), q_{h} ∣_{K} \in P_{1} ((), K), \forall K \in τ_{h}) . \end{array}

…”

Section: The Decoupled Stabilized Characteristic Finite Element Methodsmentioning

confidence: 99%

“…Here h denotes the mesh size. To solve our problem, we use the following finite element subspace W h = H fh × H ph ⊂ W and Q h ⊂ Q [11]:…”

Section: The Decoupled Stabilized Characteristic Finite Element Methodsmentioning

confidence: 99%

“…In this section, we will derive the error estimate of the CSFEM. First, we assume that the solution ( u , p , ϕ ) of problems – satisfies the following regularity hypotheses :

\begin{array}{l} ((), 1) boldu \in L^{\infty} ((),,, 0, T, H^{2} {(Ω_{f})}^{2}), ϕ \in L^{\infty} ((),,, 0, T, H^{2} ((), {normalΩ}_{p})), \\ ((), 2) u_{t} \in L^{2} ((),,, 0, T, H^{2} {(Ω_{f})}^{2}), ϕ_{t} \in L^{2} ((),,, 0, T, H^{2} ((), {normalΩ}_{p})), \\ ((), 3) p \in L^{\infty} ((),,, 0, T, H^{1} ((), {normalΩ}_{f})), p_{t} \in L^{2} ((),,, 0, T, H^{1} ((), {normalΩ}_{f})) . \end{array}

…”

Section: The Error Analysismentioning

confidence: 99%

“…In this section, we will derive the error estimate of the CSFEM. First, we assume that the solution (u, p, ) of problems (2.1)-(2.6) satisfies the following regularity hypotheses [11]:…”

Section: The Error Analysismentioning

confidence: 99%

See 2 more Smart Citations

Decoupled characteristic stabilized finite element method for time‐dependent Navier–Stokes/Darcy model

Jia

2018

Numerical Methods Partial

View full text Add to dashboard Cite

show abstract

“…Compare to Navier-Stokes model, the convection term causes some difficulties in theoretical analysis and numerical simulation. To deal with convection term, the assumption u • n f > 0 is used [6,9]. Our proposed method not only relax the influence of parameters but also improves the mass conservation.…”

mentioning

confidence: 99%

Numerical analysis of modular grad-div stability methods for the time-dependent Navier-Stokes/Darcy model

Wang

Meng

Jia

2020

era

View full text Add to dashboard Cite

In this paper, we construct a modular grad-div stabilization method for the Navier-Stokes/Darcy model, which is based on the first order Backward Euler scheme. This method does not enlarge the accuracy of numerical solution, but also can improve mass conservation and relax the influence of parameters. Herein, we give stability analysis and error estimations. Finally, by some numerical experiment, the scheme our proposed is shown to be valid.

show abstract

Decoupled modified characteristic finite element method with different subdomain time steps for nonstationary dual–porosity–Navier–Stokes model

Cao

et al. 2021

Applied Numerical Mathematics

View full text Add to dashboard Cite

A Decoupling Method with Different Subdomain Time Steps for the Non-Stationary Navier-Stokes ⁄ Darcy Model

Cited by 7 publications

References 0 publications

Decoupled characteristic stabilized finite element method for time‐dependent Navier–Stokes/Darcy model

Decoupled characteristic stabilized finite element method for time‐dependent Navier–Stokes/Darcy model

Numerical analysis of modular grad-div stability methods for the time-dependent Navier-Stokes/Darcy model

Decoupled modified characteristic finite element method with different subdomain time steps for nonstationary dual–porosity–Navier–Stokes model

Contact Info

Product

Resources

About