The fictitious domain method for the Stokes problem with Neumann/free-traction boundary condition
We consider the fictitious domain method for the Stokes problem with Neumann/free-traction boundary condition. For the penalty method, we obtain the error estimate of order O ( ϵ ) , where ϵ is the penalty parameter. Next, we apply the finite element method to the penalty problem using the P1/P1 ele...
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| Vydáno v: | Japan journal of industrial and applied mathematics Ročník 34; číslo 2; s. 585 - 610 |
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| Hlavní autor: | |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Tokyo
Springer Japan
01.08.2017
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| Témata: | |
| ISSN: | 0916-7005, 1868-937X |
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| Abstract | We consider the fictitious domain method for the Stokes problem with Neumann/free-traction boundary condition. For the penalty method, we obtain the error estimate of order
O
(
ϵ
)
, where
ϵ
is the penalty parameter. Next, we apply the finite element method to the penalty problem using the P1/P1 element with stabilization, and obtain the error estimate of discretization. The theoretical results are verified by the numerical experiments. |
|---|---|
| AbstractList | We consider the fictitious domain method for the Stokes problem with Neumann/free-traction boundary condition. For the penalty method, we obtain the error estimate of order
O
(
ϵ
)
, where
ϵ
is the penalty parameter. Next, we apply the finite element method to the penalty problem using the P1/P1 element with stabilization, and obtain the error estimate of discretization. The theoretical results are verified by the numerical experiments. |
| Author | Zhou, Guanyu |
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| Keywords | Finite element method Stokes problem Error estimate Fictitious domain method Primary 65N85 Penalty method 65N30 34M40 |
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| References | Zhou (CR23) 2017; 115 Maury (CR14) 2009; 47 Ciarlet, Ciarlet, Lions (CR5) 1991 Kashiwabara, Oikawa, Zhou (CR12) 2016; 134 Mignot (CR15) 1968; 40 Agmon, Douglis, Nirenberg (CR1) 1959; 12 Glowinski, Pan, Wells, Zhou (CR10) 1996; 126 Glowinski, Pan, Hesla, Joseph, Périaux (CR9) 2001; 169 Wloka (CR21) 1987 Angot, Bruneau, Fabrie (CR4) 1999; 81 Ramière, Angot, Belliard (CR16) 2007; 196 Saito (CR18) 2004; 40 Glowinski, Pan, Périaux (CR11) 1997; 324 Angot (CR3) 2010; 348 Zhou, Kashiwabara, Oikawa (CR24) 2016; 68 Shibata, Shimizu (CR19) 2003; 16 Angot (CR2) 2005; 341 Ramière, Angot, Belliard (CR17) 2007; 225 Zhou, Saito (CR26) 2015; 36 Massing, Larson, Logg, Rognes (CR13) 2014; 61 Tabata (CR20) 2001; 18 Clément (CR6) 1975; 9 Glowinski, Pan, Hesla, Joseph (CR8) 1999; 25 Girault, Raviart (CR7) 1986 Zhang (CR22) 2008; 46 Zhou, Saito (CR25) 2014; 31 G Zhou (255_CR26) 2015; 36 P Angot (255_CR2) 2005; 341 M Tabata (255_CR20) 2001; 18 I Ramière (255_CR16) 2007; 196 G Zhou (255_CR23) 2017; 115 S Zhang (255_CR22) 2008; 46 R Glowinski (255_CR11) 1997; 324 R Glowinski (255_CR10) 1996; 126 N Saito (255_CR18) 2004; 40 R Glowinski (255_CR8) 1999; 25 B Maury (255_CR14) 2009; 47 AL Mignot (255_CR15) 1968; 40 R Glowinski (255_CR9) 2001; 169 A Massing (255_CR13) 2014; 61 G Zhou (255_CR25) 2014; 31 PG Ciarlet (255_CR5) 1991 I Ramière (255_CR17) 2007; 225 G Zhou (255_CR24) 2016; 68 P Clément (255_CR6) 1975; 9 Y Shibata (255_CR19) 2003; 16 S Agmon (255_CR1) 1959; 12 T Kashiwabara (255_CR12) 2016; 134 V Girault (255_CR7) 1986 P Angot (255_CR3) 2010; 348 J Wloka (255_CR21) 1987 P Angot (255_CR4) 1999; 81 |
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| Title | The fictitious domain method for the Stokes problem with Neumann/free-traction boundary condition |
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