Galerkin time-stepping methods for nonlinear parabolic equations

被引：47

作者：

Akrivis, G ^{[1
]}

Makridakis, C

机构：

[1] Univ Ioannina, Dept Comp Sci, GR-45110 Ioannina, Greece

[2] Univ Crete, Dept Appl Math, Iraklion 71409, Crete, Greece

[3] FORTH, Inst Appl & Computat Math, Iraklion 71110, Crete, Greece

来源：

ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE | 2004年 / 38卷 / 02期

关键词：

nonlinear parabolic equations; local Lipschitz condition; continuous and discontinuous Galerkin methods; a priori error analysis; monotone operators;

D O I：

10.1051/m2an:2004013

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider discontinuous as well as continuous Calerkin methods for the time discretization of a class of nonlinear parabolic equations. We show existence and local uniqueness and derive optimal order optimal regularity a priori error estimates. We establish the results in an abstract Hilbert space setting and apply them to a quasilinear parabolic equation.

引用

页码：261 / 289

页数：29

共 18 条

[1]

Akrivis G, 2004, MATH COMPUT, V73, P613, DOI 10.1090/S0025-5718-03-01573-4

[2] Implicit-explicit multistep methods for quasilinear parabolic equations [J].

Akrivis, G ;

Crouzeix, M ;

Makridakis, C .

NUMERISCHE MATHEMATIK, 1999, 82 (04) :521-541

[3] Implicit-explicit multistep finite element methods for nonlinear parabolic problems [J].

Akrivis, G ;

Crouzeix, M ;

Makridakis, C .

MATHEMATICS OF COMPUTATION, 1998, 67 (222) :457-477

[4]

AKRIVIS G, 2002, CONVERGENCE TIME DIS

[5]

AZIZ AK, 1989, MATH COMPUT, V52, P255, DOI 10.1090/S0025-5718-1989-0983310-2

[6] EFFICIENT HIGHER-ORDER SINGLE STEP METHODS FOR PARABOLIC PROBLEMS .1. [J].

BRAMBLE, JH ;

SAMMON, PH .

MATHEMATICS OF COMPUTATION, 1980, 35 (151) :655-677

[7] Adaptive finite element methods for parabolic problems - VI: Analytic semigroups [J].

Eriksson, K ;

Johnson, C ;

Larsson, S .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 1998, 35 (04) :1315-1325

[8] ADAPTIVE FINITE-ELEMENT METHODS FOR PARABOLIC PROBLEMS .1. A LINEAR-MODEL PROBLEM [J].

ERIKSSON, K ;

JOHNSON, C .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 1991, 28 (01) :43-77

[9] ADAPTIVE FINITE-ELEMENT METHODS FOR PARABOLIC PROBLEMS .4. NONLINEAR PROBLEMS [J].

ERIKSSON, K ;

JOHNSON, C .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 1995, 32 (06) :1729-1749

[10]

ESTEP D., 1993, RAIRO-MATH MODEL NUM, V27, P35

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