An adaptive algorithm for the Thomas-Fermi equation

Shengfeng Zhu; Hancan Zhu; Qingbiao Wu; Yasir Khan

doi:10.1007/s11075-011-9494-1

An adaptive algorithm for the Thomas-Fermi equation

Shengfeng Zhu^*
, Hancan Zhu
, Qingbiao Wu
, Yasir Khan

^*Corresponding author for this work

School of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

20 Scopus citations

Abstract

A free boundary value problem is introduced to approximate the original Thomas-Fermi equation. The unknown truncated free boundary is determined iteratively. We transform the free boundary value problem to a nonlinear boundary value problem defined on [0,1]. We present an adaptive algorithm to solve the problem by means of the moving mesh finite element method. Comparison of our numerical results with those obtained by other approaches shows high accuracy of our method.

Original language	English
Pages (from-to)	359-372
Number of pages	14
Journal	Numerical Algorithms
Volume	59
Issue number	3
DOIs	https://doi.org/10.1007/s11075-011-9494-1
State	Published - Mar 2012

Keywords

Adaptive finite element method
Equidistribution
Free boundary value problem
Moving mesh method
Semi-infinite interval
Thomas-Fermi equation

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10.1007/s11075-011-9494-1

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abstract = "A free boundary value problem is introduced to approximate the original Thomas-Fermi equation. The unknown truncated free boundary is determined iteratively. We transform the free boundary value problem to a nonlinear boundary value problem defined on [0,1]. We present an adaptive algorithm to solve the problem by means of the moving mesh finite element method. Comparison of our numerical results with those obtained by other approaches shows high accuracy of our method.",

keywords = "Adaptive finite element method, Equidistribution, Free boundary value problem, Moving mesh method, Semi-infinite interval, Thomas-Fermi equation",

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AU - Zhu, Hancan

AU - Wu, Qingbiao

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AB - A free boundary value problem is introduced to approximate the original Thomas-Fermi equation. The unknown truncated free boundary is determined iteratively. We transform the free boundary value problem to a nonlinear boundary value problem defined on [0,1]. We present an adaptive algorithm to solve the problem by means of the moving mesh finite element method. Comparison of our numerical results with those obtained by other approaches shows high accuracy of our method.

KW - Adaptive finite element method

KW - Equidistribution

KW - Free boundary value problem

KW - Moving mesh method

KW - Semi-infinite interval

KW - Thomas-Fermi equation

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JO - Numerical Algorithms

JF - Numerical Algorithms

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ER -

An adaptive algorithm for the Thomas-Fermi equation

Abstract

Keywords

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