ERROR ESTIMATES FOR A NUMERICAL METHOD FOR THE COMPRESSIBLE NAVIER-STOKES SYSTEM ON SUFFICIENTLY SMOOTH DOMAINS

被引：14

作者：

Feireisl, Eduard ^{[1
,2
]}

Hosek, Radim ^{[1
,2
]}

Maltese, David ^{[1
,2
]}

Novotny, Antonin ^{[1
,2
]}

机构：

[1] Acad Sci Czech Republ, Inst Math, Zitna 25, CR-11567 Prague 1, Czech Republic

[2] Univ Toulon & Var, Inst Math Toulon, EA2134, BP 20132, F-83957 La Garde, France

来源：

ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE | 2017年 / 51卷 / 01期

基金：

欧洲研究理事会;

关键词：

Navier-Stokes system; finite element numerical method; finite volume numerical method; error estimates; FINITE-ELEMENT-METHOD; SUITABLE WEAK SOLUTIONS; BOUNDARY-VALUE-PROBLEMS; VOLUME SCHEMES; EQUATIONS; SOLVABILITY;

D O I：

10.1051/m2an/2016022

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We derive an a priori error estimate for the numerical solution obtained by time and space discretization by the finite volume/finite element method of the barotropic Navier-Stokes equations. The numerical solution on a convenient polyhedral domain approximating a sufficiently smooth bounded domain is compared with an exact solution of the barotropic Navier-Stokes equations with a bounded density. The result is unconditional in the sense that there are no assumed bounds on the numerical solution. It is obtained by the combination of discrete relative energy inequality derived in [T. Gallouet, R. Herbin, D. Maltese and A. Novotny, IMA J. Numer. Anal. 36 (2016) 543-592.] and several recent results in the theory of compressible Navier-Stokes equations concerning blow up criterion established in [Y. Sun, C. Wang and Z. Zhang, J. Math. Pures Appl. 95 (2011) 36-47] and weak strong uniqueness principle established in [E. Feireisl, B.J. Jin and A. Novotny, J. Math. Fluid Mech. 14 (2012) 717-730].

引用

页码：279 / 319

页数：41

共 45 条

[1] Adams R.A., 1975, Sobolev Spaces
[2] Brezzi F., 1991, SPRINGER SERIES COMP, V15
[3] Cances C., 2013, HALHAL00798287
[4] Unique solvability of the initial boundary value problems for compressible viscous fluids
Cho, Y
Choe, HJ
Kim, H
[J]. JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2004, 83 (02): : 243 - 275
[5] CROUZEIX M, 1973, REV FR AUTOMAT INFOR, V7, P33
[6] DAFERMOS CM, 1979, ARCH RATION MECH AN, V70, P167, DOI 10.1007/BF00250353
[7] On the solvability of the compressible Navier-Stokes system in bounded domains
Danchin, Raphael
[J]. NONLINEARITY, 2010, 23 (02) : 383 - 407
[8] Optimal Lp-Lq-estimates for parabolic boundary value problems with inhomogeneous data
Denk, Robert
Hieber, Matthias
Pruess, Jan
[J]. MATHEMATISCHE ZEITSCHRIFT, 2007, 257 (01) : 193 - 224
[9] Evans LC., 2018, Measure Theory and Fine Properties of Functions
[10] Error estimates for the approximate solutions of a nonlinear hyperbolic equation given by finite volume schemes
Eymard, R
Gallouet, T
Ghilani, M
Herbin, R
[J]. IMA JOURNAL OF NUMERICAL ANALYSIS, 1998, 18 (04) : 563 - 594

← 1 2 3 4 5 →