Finite volume scheme and renormalized solutions for nonlinear elliptic Neumann problem with L1 data

被引：0

作者：

Aoun, Mirella ^{[1
]}

Guibe, Olivier ^{[1
]}

机构：

[1] Univ Rouen Normandie, CNRS, Lab Math Raphael Salem, UMR 6085, F-76000 Rouen, France

来源：

CALCOLO | 2024年 / 61卷 / 03期

关键词：

Convection-diffusion equation; Finite volume schemes; Renormalized solution; Neumann boundary conditions; Integrable data; Numerical analysis; H-CONVERGENCE; EQUATIONS;

D O I：

10.1007/s10092-024-00602-3

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we study the convergence of a finite volume approximation of a convective diffusive elliptic problem with Neumann boundary conditions and L-1 data. To deal with the non-coercive character of the equation and the low regularity of the right hand-side we mix the finite volume tools and the renormalized techniques. To handle the Neumann boundary conditions we choose solutions having a null median and we prove a convergence result.

引用

页数：41

共 27 条

[1] Well-posed elliptic Neumann problems involving irregular data and domains [J].

Alvino, Angelo ;

Cianchi, Andrea ;

Maz'ya, Vladimir G. ;

Mercaldo, Anna .

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2010, 27 (04) :1017-1054

[2]

[Anonymous], 1999, FINITE VOLUMES COMPL

[3]

Aoun M., Approximation of elliptic, parabolic equations with data and Neumann boundary condition

[4] On discrete functional inequalities for some finite volume schemes [J].

Bessemoulin-Chatard, Marianne ;

Chainais-Hillairet, Claire ;

Filbet, Francis .

IMA JOURNAL OF NUMERICAL ANALYSIS, 2015, 35 (03) :1125-1149

[5] Neumann problems for nonlinear elliptic equations with L1 data [J].

Betta, M. F. ;

Guibe, O. ;

Mercaldo, A. .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2015, 259 (03) :898-924

[6] UNIQUENESS FOR NEUMANN PROBLEMS FOR NONLINEAR ELLIPTIC EQUATIONS [J].

Betta, Maria Francesca ;

Guibe, Olivier ;

Mercaldo, Anna .

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2019, 18 (03) :1023-1048

[7] NON-LINEAR ELLIPTIC AND PARABOLIC EQUATIONS INVOLVING MEASURE DATA [J].

BOCCARDO, L ;

GALLOUET, T .

JOURNAL OF FUNCTIONAL ANALYSIS, 1989, 87 (01) :149-169

[8] Finite elements approximation of second order linear elliptic equations in divergence form with right-hand side in L1 [J].

Casado-Diaz, J. ;

Rebollo, T. Chacon ;

Girault, V. ;

Marmol, M. Gomez ;

Murat, F. .

NUMERISCHE MATHEMATIK, 2007, 105 (03) :337-374

[9] Finite volume scheme for multi-dimensional drift-diffusion equations and convergence analysis [J].

Chainais-Hillairet, C ;

Liu, JG ;

Peng, YJ .

ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE, 2003, 37 (02) :319-338

[10] Finite-volume schemes for noncoercive elliptic problems with Neumann boundary conditions [J].

Chainais-Hillairet, Claire ;

Droniou, Jerome .

IMA JOURNAL OF NUMERICAL ANALYSIS, 2011, 31 (01) :61-85

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