Estimate of Convergence Rate of the Galerkin Method for a Nonclassical Equation of Mathematical Physics

被引：0

作者：

Fedorov, Valery E. ^{[1
]}

机构：

[1] North Eastern Fed Univ, 58 Belinskogo Str, Yakutsk 677000, Russia

来源：

2D SYSTEMS OF THE STRONG CORRELATED ELECTRONS: FROM FUNDAMENTAL RESEARCH TO PRACTICAL APPLICATIONS | 2018年 / 2041卷

关键词：

D O I：

10.1063/1.5079376

中图分类号：

O59 [应用物理学];

学科分类号：

摘要：

In this paper author prove the existence and uniqueness of a regular solution of the first boundary value problem for a higher order nonclassical equation of mathematical physics in a cylindrical domain, using the nonstationary Galerkin method and regularization method. The estimate is obtained for convergence rate of approximate solutions of this problem in terms of regularization parameter and eigenvalues of the selfadjoint spectral problem for a higher order elliptic equation.

引用

页数：4

共 50 条

[41] ON THE RATE OF CONVERGENCE OF THE NONLINEAR GALERKIN METHODS [J].

DEVULDER, C ;

MARION, M ;

TITI, ES .

MATHEMATICS OF COMPUTATION, 1993, 60 (202) :495-514

[42] Convergence of the spectral Galerkin method for the stochastic reaction-diffusion-advection equation [J].

Yang, Li ;

Zhang, Yanzhi .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2017, 446 (02) :1230-1254

[43] CONVERGENCE OF A DISCONTINUOUS GALERKIN METHOD FOR THE MISCIBLE DISPLACEMENT EQUATION UNDER LOW REGULARITY [J].

Riviere, Beatrice M. ;

Walkington, Noel J. .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 2011, 49 (03) :1085-1110

[44] Weighted estimate for the convergence rate of a projection difference scheme for a quasilinear parabolic equation [J].

V. A. Grebennikov ;

A. V. Razgulin .

Computational Mathematics and Mathematical Physics, 2011, 51 :1208-1221

[45] CONVERGENCE AND ERROR ESTIMATION IN NETWORK METHOD FOR NONLINEAR PROBLEMS OF MATHEMATICAL PHYSICS [J].

ABRASHIN, VN .

DOKLADY AKADEMII NAUK BELARUSI, 1973, 17 (11) :984-987

[46] Convergence of the Galerkin method for a wave equation with singular right-hand side [J].

Nomirovs'kyi D.A. .

Ukrainian Mathematical Journal, 2006, 58 (6) :876-886

[47] Weighted estimate for the convergence rate of a projection difference scheme for a quasilinear parabolic equation [J].

Grebennikov, V. A. ;

Razgulin, A. V. .

COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS, 2011, 51 (07) :1208-1221

[48] Convergence analysis of an adaptive interior penalty discontinuous Galerkin method for the Helmholtz equation [J].

Hoppe, R. H. W. ;

Sharma, N. .

IMA JOURNAL OF NUMERICAL ANALYSIS, 2013, 33 (03) :898-921

[49] THE CONVERGENCE OF A MODIFICATION OF THE GALERKIN METHOD [J].

ZHDANOV, GA .

DOKLADY AKADEMII NAUK SSSR, 1957, 115 (02) :223-225

[50] NONUNIFORM CONVERGENCE OF GALERKIN METHOD [J].

LEIPHOLZ, HHE ;

MANDADI, R .

JOURNAL OF SOUND AND VIBRATION, 1978, 57 (04) :483-498

← 1 2 3 4 5 →