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Rate of Convergence of Particular Approximate Solutions of Elliptic Boundary- and Eigenvalue Problems on Regions with Corners

机译：具有角的区域上椭圆边值问题和特征值问题特殊近似解的收敛速度

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摘要

The author considers boundary- and eigenvalue problems with elliptic operators L on a domain G contained in Euclidean 2-space. By using Vekua's theory and approximation theory, the approximation properties of some special classes of solutions u of Lu = 0 on G are studied. Here, one is particularly interested in investigations of the approximation properties of certain trial functions which have singularities at corners of G. Applied to defect-minimization methods for solving boundary- and eigenvalue problems, this theory provides one with a class of trial functions which can be easily adapted to a given problem. In special situations, the method produces approximations with extremely high accuracy by using only few trial functions.

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作者
Still, G. J.;
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年度 1990
页码 p.1-43
总页数 43
原文格式 PDF
正文语种 eng
中图分类工业技术;
关键词
Elliptic differential equations ; Boundary value problems ; Analytic functions ; Numerical solution ; Approximation ; Singularity ; Eigenvalues ; Laplacian ; Convergence ; Theorems;

机译：椭圆微分方程;边值问题;解析函数;数值解;逼近;奇异性;特征值;拉普拉斯算子;收敛性;定理;

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专利

1. Consistent Convergence Rate Estimates in the Grid W-2,0(2)(omega) Norm for Difference Schemes Approximating Nonlinear Elliptic Equations with Mixed Derivatives and Solutions from W-2,0(m)(Omega), 3< m <= 4 [J] . Lubyshev F. V., Fairuzov M. E. Computational mathematics and mathematical physics . 2017,第9期

机译：Grid W-2,0（2）（Omega）规范的一致收敛速率估计是近似非线性椭圆方程与W-2,0（m）（ω）的混合衍生物和溶液，3
2. On the solution of elliptic partial differential equations on regions with corners Ⅱ: Detailed analysis [J] . Serkh Kirill Applied and Computational Harmonic Analysis . 2019,第2期

机译：关于带有角的区域上的椭圆型偏微分方程的求解Ⅱ：详细分析
3. On the solution of elliptic partial differential equations on regions with corners [J] . Serkh Kirill, Rokhlin Vladimir Journal of Computational Physics . 2016,第Null期

机译：关于有角区域上的椭圆型偏微分方程的解
4. EXISTENCE OF SOLUTIONS AND POSITIVITY OF THE INFIMUM EIGENVALUE FOR DEGENERATE ELLIPTIC EQUATIONS WITH VARIABLE EXPONENTS [C] . Inbo Sim, Yun-Ho Kim AIMS International Conference on Dynamical Systems, Differential Equations and Applications . 2013

机译：可变指数的退化椭圆方程的最终椭圆方程的溶液与阳性的存在性
5. On the Solution of Elliptic Partial Differential Equations on Regions with Corners. [D] . Serkh, Kirill. 2016

机译：关于带角区域上的椭圆型偏微分方程的解。
6. Multiple Solutions for a Class of Dirichlet Double Eigenvalue Quasilinear Elliptic Systems Involving the (p1… pn)-Laplacian Operator [O] . Armin Hadjian, Saleh Shakeri 2013

机译：一类Dirichlet双特征值拟线性椭圆系统的多重解其中（p1…pn）-拉普拉斯算子
7. Strong convergence and convergence rates of approximating solutions for algebraic Riccati equations in Hilbert spaces [O] . Ito Kazufumi 1987

机译：Hilbert空间中代数Riccati方程的强收敛性和逼近解的收敛速度
8. Solution of Elliptic Partial Differential Equations on Regions with Corners. [R] . Serkh, K., Rokhlin, V. 2015

机译：具有角的区域上椭圆偏微分方程的解。

Rate of Convergence of Particular Approximate Solutions of Elliptic Boundary- and Eigenvalue Problems on Regions with Corners

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