An unsaturated numerical method for the exterior axisymmetric Neumann problem for Laplace’s equation

被引:0
作者
V. N. Belykh
机构
[1] Sobolev Institute of Mathematics,
来源
Siberian Mathematical Journal | 2011年 / 52卷
关键词
Laplace equation; Neumann problem; unsaturated numerical method; exponential convergence;
D O I
暂无
中图分类号
学科分类号
摘要
Basing on the fundamental ideas of Babenko, we construct a fundamentally new, unsaturated, numerical method for solving the axially symmetric exterior Neumann problem for Laplace’s equation. The distinctive feature of this method is the absence of the principal error term enabling us to automatically adjust to every class of smoothness of solutions natural in the problem.
引用
收藏
页码:980 / 994
页数:14
相关论文
共 50 条
[21]   Superconvergent Algorithms for the Numerical Solution of the Laplace Equation in Smooth Axisymmetric Domains [J].
V. N. Belykh .
Computational Mathematics and Mathematical Physics, 2020, 60 :545-557
[22]   Transmission problem for the Laplace equation and the integral equation method [J].
Medkova, D. .
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2012, 387 (02) :837-843
[23]   A Method for Solving an Exterior Boundary Value Problem for the Laplace Equation by Overlapping Domain Decomposition [J].
Savchenko A.O. ;
Petukhov A.V. .
Journal of Applied and Industrial Mathematics, 2019, 13 (03) :519-527
[24]   A method for solving an exterior three-dimensional boundary value problem for the Laplace equation [J].
Savchenko A.O. ;
Il’in V.P. ;
Butyugin D.S. .
Journal of Applied and Industrial Mathematics, 2016, 10 (02) :277-287
[25]   On the spectrum of the Neumann problem for Laplace equation in a domain with a narrow slit [J].
Gadyl'shin, Rustem R. ;
Il'in, Arlen M. .
ASYMPTOTIC ANALYSIS, 2010, 67 (3-4) :167-189
[26]   Dirichlet or Neumann Problem for Weighted 1-Laplace Equation with Application to Image Denoising [J].
X. Fu ;
J. Xiao ;
Q. Xiong .
The Journal of Geometric Analysis, 2024, 34
[27]   The Mixed Problem for the Laplace Equation in an Exterior Domain with an Arbitrary Partition of the Boundary [J].
P. A. Krutitskii .
Mathematical Notes, 2001, 69 :799-813
[28]   The mixed problem for the laplace equation in an exterior domain with an arbitrary partition of the boundary [J].
Krutitskii, PA .
MATHEMATICAL NOTES, 2001, 69 (5-6) :799-813
[29]   The Integral Equation Method and the Neumann Problem for the Poisson Equation on NTA Domains [J].
Medkova, Dagmar .
INTEGRAL EQUATIONS AND OPERATOR THEORY, 2009, 63 (02) :227-247
[30]   Shape differentiability of the Neumann problem of the Laplace equation in the half-space [J].
Amrouche, Cherif ;
Necasova, Sarka ;
Sokolowski, Jan .
CONTROL AND CYBERNETICS, 2008, 37 (04) :747-769