A priori and a posteriori estimates of the stabilized finite element methods for the incompressible flow with slip boundary conditions arising in arteriosclerosis

被引：1

作者：

Li, Jian ^{[1
]}

Zheng, Haibiao ^{[2
]}

Zou, Qingsong ^{[3
,4
]}

机构：

[1] Shaanxi Univ Sci & Technol, Sch Arts & Sci, Dept Math, Xian, Shaanxi, Peoples R China

[2] East China Normal Univ, Shanghai Key Lab Pure Math & Math Practice, Sch Math Sci, Shanghai, Peoples R China

[3] Sun Yat Sen Univ, Sch Data & Computat Sci, Guangzhou, Guangdong, Peoples R China

[4] Sun Yat Sen Univ, Guangdong Prov Key Lab Computat Sci, Guangzhou, Guangdong, Peoples R China

来源：

ADVANCES IN DIFFERENCE EQUATIONS | 2019年 / 2019卷 / 01期

关键词：

Stokes equations; Slip boundary condition; Variational inequality; Finite element methods; A priori error estimates; A posteriori error estimates; Numerical experiments; NAVIER-STOKES EQUATIONS; LOCAL GAUSS INTEGRATIONS; PRESSURE PROJECTION; ERROR ESTIMATORS; VOLUME METHODS; LEAK; APPROXIMATIONS; REGULARITY;

D O I：

10.1186/s13662-019-2312-0

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we develop the lower order stabilized finite element methods for the incompressible flow with the slip boundary conditions of friction type whose weak solution satisfies a variational inequality. The H-1-norm for the velocity and the L-2-norm for the pressure decrease with optimal convergence order. The reliable and efficient a posteriori error estimates are also derived. Finally, numerical experiments are presented to validate the theoretical results.

引用

页数：20

共 50 条

[31] A posteriori error estimates with boundary correction for a cut finite element method
Burman, Erik
He, Cuiyu
Larson, Mats G.
IMA JOURNAL OF NUMERICAL ANALYSIS, 2022, 42 (01) : 333 - 362
[32] A priori and a posteriori estimates for three-dimensional Stokes equations with nonstandard boundary conditions
Abboud, Hyam
El Chami, Fida
Sayah, Toni
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2012, 28 (04) : 1178 - 1193
[33] Spectral Element Methods a Priori and a Posteriori Error Estimates for Penalized Unilateral Obstacle Problem
Bochra Djeridi
Radouen Ghanem
Hocine Sissaoui
Journal of Scientific Computing, 2020, 85
[34] A POSTERIORI ERROR ESTIMATES OF A NON-CONFORMING FINITE ELEMENT METHOD FOR PROBLEMS WITH ARTIFICIAL BOUNDARY CONDITIONS
Xianmin Xu and Zhiping Li LMAM & School of Mathematical Sciences
JournalofComputationalMathematics, 2009, 27 (06) : 677 - 696
[35] A POSTERIORI ERROR ESTIMATES OF A NON-CONFORMING FINITE ELEMENT METHOD FOR PROBLEMS WITH ARTIFICIAL BOUNDARY CONDITIONS
Xu, Xianmin
Li, Zhiping
JOURNAL OF COMPUTATIONAL MATHEMATICS, 2009, 27 (06) : 677 - 696
[36] Spectral Element Methods a Priori and a Posteriori Error Estimates for Penalized Unilateral Obstacle Problem
Djeridi, Bochra
Ghanem, Radouen
Sissaoui, Hocine
JOURNAL OF SCIENTIFIC COMPUTING, 2020, 85 (03)
[37] Pressure projection stabilized finite element method for Stokes problem with nonlinear slip boundary conditions
Li, Yuan
Li, Kaitai
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2011, 235 (12) : 3673 - 3682
[38] Stabilized finite element formulation for incompressible flow on distorted meshes
Foerster, Ch.
Wall, W. A.
Ramm, E.
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, 2009, 60 (10) : 1103 - 1126
[39] A POSTERIORI ERROR ESTIMATE FOR STABILIZED FINITE ELEMENT METHODS FOR THE STOKES EQUATIONS
Wang, Junping
Wang, Yanqiu
Ye, Xiu
INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING, 2012, 9 (01) : 1 - 16
[40] A posteriori error estimates for mixed finite element and finite volume methods for problems coupled through a boundary with nonmatching grids
Arbogast, T.
Estep, D.
Sheehan, B.
Tavener, S.
IMA JOURNAL OF NUMERICAL ANALYSIS, 2014, 34 (04) : 1625 - 1653

← 1 2 3 4 5 →