Approximation of time-dependent viscoelastic fluid flow: SUPG approximation

被引：45
作者：
Ervin, VJ [1 ]
Miles, WW [1 ]
机构：
[1] Clemson Univ, Dept Math Sci, Clemson, SC 29634 USA
来源：
SIAM JOURNAL ON NUMERICAL ANALYSIS | 2003年 / 41卷 / 02期
关键词：
viscoelasticity; finite element method; fully discrete; SUPG;
D O I：
10.1137/S003614290241177X
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this article we consider the numerical approximation to the time-dependent viscoelasticity equations with an Oldroyd B constitutive equation. The approximation is stabilized by using a streamline upwind Petrov - Galerkin (SUPG) approximation for the constitutive equation. We analyze both the semidiscrete and fully discrete numerical approximations. For both discretizations we prove the existence of, and derive a priori error estimates for, the numerical approximations.
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页码：457 / 486
页数：30
相关论文
共 14 条
[1]   FINITE-ELEMENT APPROXIMATION OF VISCOELASTIC FLUID-FLOW - EXISTENCE OF APPROXIMATE SOLUTIONS AND ERROR-BOUNDS .1. DISCONTINUOUS CONSTRAINTS [J].
BARANGER, J ;
SANDRI, D .
NUMERISCHE MATHEMATIK, 1992, 63 (01) :13-27
[2]   Existence of approximate solutions and error bounds for viscoelastic fluid flow: Characteristics method [J].
Baranger, J ;
Machmoum, A .
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 1997, 148 (1-2) :39-52
[3]   NUMERICAL-ANALYSIS OF A FEM FOR A TRANSIENT VISCOELASTIC FLOW [J].
BARANGER, J ;
WARDI, S .
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 1995, 125 (1-4) :171-185
[4]  
Bird R. B., 1987, DYNAMICS POLYM LIQUI, V1
[5]  
Brenner S. C., 2007, Texts Appl. Math., V15
[6]  
CORDUNEANU C, 1977, PRINCIPALS DIFFERENT
[7]  
Girault V., 2012, FINITE ELEMENT METHO, V5
[8]   EXISTENCE RESULTS FOR THE FLOW OF VISCOELASTIC FLUIDS WITH A DIFFERENTIAL CONSTITUTIVE LAW [J].
GUILLOPE, C ;
SAUT, JC .
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1990, 15 (09) :849-869
[9]   FINITE-ELEMENT APPROXIMATION OF THE NONSTATIONARY NAVIER-STOKES PROBLEM .4. ERROR ANALYSIS FOR 2ND-ORDER TIME DISCRETIZATION [J].
HEYWOOD, JG ;
RANNACHER, R .
SIAM JOURNAL ON NUMERICAL ANALYSIS, 1990, 27 (02) :353-384
[10]   A two-level method with backtracking for the Navier-Stokes equations [J].
Layton, W ;
Tobiska, L .
SIAM JOURNAL ON NUMERICAL ANALYSIS, 1998, 35 (05) :2035-2054
12