On a two-grid finite element scheme combined with Crank-Nicolson method for the equations of motion arising in the Kelvin-Voigt model

被引：18

作者：

Bajpai, S. ^{[1
]}

Nataraj, N. ^{[2
]}

机构：

[1] Tata Inst Fundamental Res Bangalore, Dept Math, Bangalore, Karnataka, India

[2] Indian Inst Technol, Dept Math, Bombay, Maharashtra, India

来源：

COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2014年 / 68卷 / 12期

关键词：

Kelvin-Voigt model; Two-grid method; Crank-Nicolson scheme; Error estimates; Optimal convergence rates; NAVIER-STOKES EQUATIONS; DISCRETIZATION;

D O I：

10.1016/j.camwa.2014.07.011

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we present a second order accurate Crank-Nicolson scheme applied to a system arising from Galerkin finite element two-grid approximations to the equations of motion described by the Kelvin-Voigtviscoelastic fluid flow model. Optimal error estimates in L-infinity(L-2)-norm and L-infinity(H-1)-norm for velocity and L-infinity(L-2)-norm for pressure are established. These estimates are shown to be uniform in time. Numerical results are provided to verify the theoretical estimates. (C) 2014 Elsevier Ltd. All rights reserved.

引用

页码：2277 / 2291

页数：15

共 17 条

[1] Two-grid finite element scheme for the fully discrete time-dependent Navier-Stokes problem [J].

Abboud, H ;

Girault, V ;

Sayah, T .

COMPTES RENDUS MATHEMATIQUE, 2005, 341 (07) :451-456

[2] A second order accuracy for a full discretized time-dependent Navier-Stokes equations by a two-grid scheme [J].

Abboud, Hyam ;

Girault, Vivette ;

Sayah, Toni .

NUMERISCHE MATHEMATIK, 2009, 114 (02) :189-231

[3] ON FULLY DISCRETE GALERKIN METHODS OF 2ND-ORDER TEMPORAL ACCURACY FOR THE NONLINEAR SCHRODINGER-EQUATION [J].

AKRIVIS, GD ;

DOUGALIS, VA ;

KARAKASHIAN, OA .

NUMERISCHE MATHEMATIK, 1991, 59 (01) :31-53

[4]

Bajpai S., 2013, ADV COMPUT IN PRESS

[5]

Bajpai S, 2013, INT J NUMER ANAL MOD, V10, P481

[6] Semidiscrete Galerkin method for equations of motion arising in Kelvin-Voigt model of viscoelastic fluid flow [J].

Bajpai, Saumya ;

Nataraj, Neela ;

Pani, Amiya K. ;

Damazio, Pedro ;

Yuan, Jin Yun .

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2013, 29 (03) :857-883

[7]

Burtscher M., 2006, 2006 INT C MOD SIM V, P101

[8] A viscoelastic fluid model for brain injuries [J].

Cotter, CS ;

Smolarkiewicz, PK ;

Szczyrba, IN .

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, 2002, 40 (1-2) :303-311

[9] A two-grid method based on Newton iteration for the Navier-Stokes equations [J].

Dai, Xiaoxia ;

Cheng, Xiaoliang .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2008, 220 (1-2) :566-573

[10] Optimal error bounds for two-grid schemes applied to the Navier-Stokes equations [J].

de Frutos, Javier ;

Garcia-Archilla, Bosco ;

Novo, Julia .

APPLIED MATHEMATICS AND COMPUTATION, 2012, 218 (13) :7034-7051

← 1 2 →