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

Jian Li; Haibiao Zheng; Qingsong Zou

doi:10.1186/s13662-019-2312-0

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

Jian Li
, Haibiao Zheng
, Qingsong Zou^*

^*Corresponding author for this work

School of Mathematical Sciences

Shaanxi University of Science and Technology
Sun Yat-Sen University

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

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 H¹-norm for the velocity and the L²-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.

Original language	English
Article number	374
Journal	Advances in Difference Equations
Volume	2019
Issue number	1
DOIs	https://doi.org/10.1186/s13662-019-2312-0
State	Published - 1 Dec 2019

Keywords

A posteriori error estimates
A priori error estimates
Finite element methods
Numerical experiments
Slip boundary condition
Stokes equations
Variational inequality

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10.1186/s13662-019-2312-0

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

abstract = "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 H1-norm for the velocity and the L2-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.",

keywords = "A posteriori error estimates, A priori error estimates, Finite element methods, Numerical experiments, Slip boundary condition, Stokes equations, Variational inequality",

author = "Jian Li and Haibiao Zheng and Qingsong Zou",

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AU - Li, Jian

AU - Zheng, Haibiao

AU - Zou, Qingsong

PY - 2019/12/1

Y1 - 2019/12/1

N2 - 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 H1-norm for the velocity and the L2-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.

AB - 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 H1-norm for the velocity and the L2-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.

KW - A posteriori error estimates

KW - A priori error estimates

KW - Finite element methods

KW - Numerical experiments

KW - Slip boundary condition

KW - Stokes equations

KW - Variational inequality

UR - https://www.scopus.com/pages/publications/85071320457

U2 - 10.1186/s13662-019-2312-0

DO - 10.1186/s13662-019-2312-0

M3 - 文章

AN - SCOPUS:85071320457

SN - 1687-1839

VL - 2019

JO - Advances in Difference Equations

JF - Advances in Difference Equations

IS - 1

M1 - 374

ER -

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

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Keywords

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