Approximate Solution of the Dirichlet Problem for Elliptic PDE and Its Error Estimate

机译：椭圆型PDE Dirichlet问题的近似解及其误差估计

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The proposed in [7] uniform error estimate allows to control the accuracy of the symbolic approximate solution of the Dirichlet problem for elliptic PDE in the whole domain of the problem considered. The present paper demonstrates the techniques of finding such an approximate solution with Mathematica and the use of the uniform error estimate for a concrete example.

机译：文献[7]中提出的均匀误差估计允许在所考虑问题的整个域内控制椭圆PDE的Dirichlet问题的符号近似解的准确性。本文演示了使用Mathematica查找这种近似解的技术以及将均匀误差估计用于具体示例的方法。

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来源
《International Workshop on Computer Algebra in Scientific Computing(CASC 2005); 20050912-16; Kalamata(GR)》|2005年|P.489-500|共12页
会议地点 Kalamata(GR)
作者
Serguey Zemskov;
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作者单位

University of Rostock;

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会议组织
原文格式 PDF
正文语种 eng
中图分类计算技术、计算机技术;代数、数论、组合理论;
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专利

1. A posteriori error estimator and indicator in generalized finite differences. Application to improve the approximated solution of elliptic PDEs [J] . J. J. BENITO, F. URENA, L. GAVETE, International journal of computer mathematics . 2008,第3a4期

机译：广义有限差分中的后验误差估计器和指示符。在改进椭圆PDE近似解中的应用
2. A POSTERIORI ERROR ESTIMATE OF APPROXIMATE SOLUTIONS TO A SPECIAL NONLINEAR ELLIPTIC BOUNDARY VALUE PROBLEM [J] . Weisz J. Zeitschrift fur Angewandte Mathematik und Mechanik . 1995,第1期

机译：特殊非线性椭圆边值问题的近似解的一个正误差估计
3. Finite Element Method and A Priori Error Estimates for Dirichlet Boundary Control Problems Governed by Parabolic PDEs [J] . Gong Wei, Hinze Michael, Zhou Zhaojie Journal of Scientific Computing . 2016,第3期

机译：抛物型偏微分方程控制Dirichlet边界控制问题的有限元方法和先验误差估计
4. Approximate Solution of the Dirichlet Problem for Elliptic PDE and Its Error Estimate [C] . International Workshop on Computer Algebra in Scientific Computing . 2005

机译：椭圆PDE的Dirichlet问题的近似解及其误差估计
5. Error estimates for finite-element solutions of elliptic boundary value problems. [D] . Mashaie, Akbar. 1990

机译：椭圆边值问题的有限元解的误差估计。
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. A posteriori error estimator and indicator in Generalized Finite Differences. Application to improve the approximated solution of elliptic pdes. [O] . Benito, Juan J, Ureña, Francisco, Gavete, Luis, 2008

机译：广义有限差分中的后验误差估计器和指示符。用于改进椭圆pdes的近似解的应用。
8. Error Bounds on Numerical Solutions of Dirichlet Problems for Quasilinear Elliptic Equations [R] . Thurman G. Frank 1967

机译：拟线性椭圆型方程Dirichlet问题数值解的误差界

Approximate Solution of the Dirichlet Problem for Elliptic PDE and Its Error Estimate

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