Three-dimensional stable nonconforming parallelepiped elements for the Stokes problem.
type: Item
instance of: scholarly article
title: Three-dimensional stable nonconforming parallelepiped elements for the Stokes problem.
zbMATH Open document ID: 1041.35060
DOI: 10.1016/S0096-3003(01)00117-5
author: Hoon Huh
author: Yongdeok Kim
author: Sungyun Lee
published in: Applied Mathematics and Computation
publication date: 2003-01-28T00:00:00Z
review text: The authors consider the system of Stokes equations: \(-\nu\Delta u+ \nabla p=f\) in \(\Omega\), \(\text{div\,}u= 0\) in \(\Omega\), \(u= 0\) on \(\partial\Omega\), where \(\Omega\in \mathbb R^3\) -- a bounded domain, \(f\) -- the given body force, \(\nu>0\) the kinematic viscosity; for simplicity, they consider \(\nu=1\). For the solution of this boundary value problem they apply the approximate method proposed by \textit{J. Douglas} et al. [Math. Model. Numer. Anal. 33, No. 4, 747--770 (1999; Zbl 0041.65115)]; it is an extension of a similar paper, published in [Appl. Math. Comput. 115, No. 2--3, 101--112 (2000; Zbl 1028.76025)] by \textit{Y. Kim} and \textit{S. Lee}, elaborated in the two-dimensional case. The plan of the paper is the following: 1) the Stokes problem is briefly reviewed in some lines at the beginning of the paper, 2) the space of finite elements approximation for the Stokes problem on parallelepiped elements is given, 3) stability results are given, using macroelement technique, 4) optimal order error estimates are derived in the final part of the paper.
reviewed by: Vasile Ionescu
Mathematics Subject Classification ID: 35Q35
Mathematics Subject Classification ID: 76M25
Mathematics Subject Classification ID: 76D07
Mathematics Subject Classification ID: 65N12
Mathematics Subject Classification ID: 65N30
zbMATH DE Number: 1861143
zbMATH Keywords: stable numerical methods
zbMATH Keywords: nonconforming parallelepiped elements
zbMATH Keywords: conforming bubble functions
zbMATH Keywords: error estimates
zbMATH Keywords: stationary Stokes boundary value problem
MaRDI profile type: Publication
cites work: Nonconforming Galerkin methods based on quadrilateral elements for second order elliptic problems
cites work: Stable nonconforming quadrilateral finite elements for the Stokes problem
cites work: Analysis of Locally Stabilized Mixed Finite Element Methods for the Stokes Problem
cites work: Simple nonconforming quadrilateral Stokes element
cites work: The stability of finite element methods
cites work: Error Analysis of some Finite Element Methods for the Stokes Problem
cites work: A stable nonconforming quadrilateral finite element method for the stationary Stokes and Navier-Stokes equations
full work available at URL: s0096-3003(01)00117-5
OpenAlex ID: W2045964922
description: scientific article; zbMATH DE number 1861143