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
收藏
页数：4
相关论文
共 50 条
[31]   Stability and convergence of the wavelet-Galerkin method for the sideways heat equation [J].
Reginska, T. ;
Elden, L. .
Journal of Inverse and Ill-Posed Problems, 2000, 8 (01) :31-49
[32]   Convergence of Galerkin method solutions of the integral equation for thin wire antennas [J].
Rynne, BP .
ADVANCES IN COMPUTATIONAL MATHEMATICS, 2000, 12 (2-3) :251-259
[33]   Convergence of Galerkin method solutions of the integral equation for thin wire antennas [J].
Bryan P. Rynne .
Advances in Computational Mathematics, 2000, 12 :251-259
[34]   Galerkin finite element method and the groundwater flow equation: 1. Convergence of the method [J].
Botha, J. F. ;
Bakkes, G. N. .
ADVANCES IN WATER RESOURCES, 1982, 5 (02) :121-126
[35]   Error Estimate of the Nonstationary Galerkin Method for a Higher Order Equation of Mixed Type [J].
Egorov, Ivan E. ;
Fedorov, Valery E. .
PROCEEDINGS OF THE 44TH INTERNATIONAL CONFERENCE "APPLICATIONS OF MATHEMATICS IN ENGINEERING AND ECONOMICS", 2018, 2048
[36]   ASYMPTOTIC ESTIMATE OF A PETROV - GALERKIN METHOD FOR NONLINEAR OPERATOR-DIFFERENTIAL EQUATION [J].
Vinogradova, P. V. ;
Samusenko, A. M. ;
Manzhula, Ls. .
BULLETIN OF THE SOUTH URAL STATE UNIVERSITY SERIES-MATHEMATICAL MODELLING PROGRAMMING & COMPUTER SOFTWARE, 2016, 9 (04) :17-29
[37]   Superconvergence error estimate of Galerkin method for Sobolev equation with Burgers' type nonlinearity [J].
Yang, Huaijun .
APPLIED NUMERICAL MATHEMATICS, 2021, 168 :13-22
[38]   RATE OF CONVERGENCE OF THE BUBNOV-GALERKIN METHOD FOR HYPERBOLIC-EQUATIONS [J].
ZHELEZOVSKAYA, LA ;
ZHELEZOVSKII, SE ;
KIRICHENKO, VF ;
KRYSKO, VA .
DIFFERENTIAL EQUATIONS, 1990, 26 (02) :251-258
[39]   RATE OF CONVERGENCE OF THE ROTA-GALERKIN METHOD FOR HYPERBOLIC-EQUATIONS [J].
ZHELEZOVSKAYA, LA ;
ZHELEZOVSKII, SE .
DIFFERENTIAL EQUATIONS, 1992, 28 (02) :261-269
[40]   QUASI-OPTIMAL CONVERGENCE RATE OF AN ADAPTIVE DISCONTINUOUS GALERKIN METHOD [J].
Bonito, Andrea ;
Nochetto, Ricardo H. .
SIAM JOURNAL ON NUMERICAL ANALYSIS, 2010, 48 (02) :734-771
12345