Splitting extrapolation algorithms for solving the boundary integral equations of anisotropic Darcy’s equation on polygons by mechanical quadrature methods

In this paper we study the stability and convergence of the solution for the first kind integral equations of the anisotropic Darcy’s equations by the mechanical quadrature methods on closed polygonal boundaries in ℝ 2 . Using the collectively compact theory, we construct numerical solutions which c...

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Veröffentlicht in:Numerical algorithms Jg. 62; H. 1; S. 27 - 43
Hauptverfasser: Luo, Xin, Huang, Jin, Wang, Chuan-Long
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Boston Springer US 01.01.2013
Springer Nature B.V
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ISSN:1017-1398, 1572-9265
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Abstract In this paper we study the stability and convergence of the solution for the first kind integral equations of the anisotropic Darcy’s equations by the mechanical quadrature methods on closed polygonal boundaries in ℝ 2 . Using the collectively compact theory, we construct numerical solutions which converge with the order , where is the mesh size. In addition, An a posteriori asymptotic error representation is derived by splitting extrapolation methods in order to construct self-adaptive algorithms, and the convergence rate can be achieved after using the splitting extrapolation methods once. Finally, the numerical examples show the efficiency of our methods.
AbstractList In this paper we study the stability and convergence of the solution for the first kind integral equations of the anisotropic Darcy’s equations by the mechanical quadrature methods on closed polygonal boundaries in ℝ 2 . Using the collectively compact theory, we construct numerical solutions which converge with the order , where is the mesh size. In addition, An a posteriori asymptotic error representation is derived by splitting extrapolation methods in order to construct self-adaptive algorithms, and the convergence rate can be achieved after using the splitting extrapolation methods once. Finally, the numerical examples show the efficiency of our methods.
In this paper we study the stability and convergence of the solution for the first kind integral equations of the anisotropic Darcy’s equations by the mechanical quadrature methods on closed polygonal boundaries in ℝ2. Using the collectively compact theory, we construct numerical solutions which converge with the order , where is the mesh size. In addition, An a posteriori asymptotic error representation is derived by splitting extrapolation methods in order to construct self-adaptive algorithms, and the convergence rate can be achieved after using the splitting extrapolation methods once. Finally, the numerical examples show the efficiency of our methods.
Author Wang, Chuan-Long
Huang, Jin
Luo, Xin
Author_xml – sequence: 1
  givenname: Xin
  surname: Luo
  fullname: Luo, Xin
  email: luoxin919@163.com
  organization: School of Mathematical Sciences, University of Electronic Science and Technology of China
– sequence: 2
  givenname: Jin
  surname: Huang
  fullname: Huang, Jin
  organization: School of Mathematical Sciences, University of Electronic Science and Technology of China
– sequence: 3
  givenname: Chuan-Long
  surname: Wang
  fullname: Wang, Chuan-Long
  organization: Department of Mathematics, Taiyuan Normal University
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CitedBy_id crossref_primary_10_1016_j_cam_2020_113339
crossref_primary_10_1016_j_cam_2018_05_065
crossref_primary_10_1155_2020_6484890
crossref_primary_10_1080_00207160_2015_1095888
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Issue 1
Keywords Anisotropic
Mechanical quadrature methods
Darcy’s equation
A posteriori estimate
Splitting extrapolation algorithm
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Snippet In this paper we study the stability and convergence of the solution for the first kind integral equations of the anisotropic Darcy’s equations by the...
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SubjectTerms Adaptive algorithms
Algebra
Algorithms
Asymptotic methods
Boundary integral method
Computer Science
Convergence
Extrapolation
Integral equations
Numeric Computing
Numerical Analysis
Numerical methods
Original Paper
Polygons
Quadratures
Splitting
Theory of Computation
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Title Splitting extrapolation algorithms for solving the boundary integral equations of anisotropic Darcy’s equation on polygons by mechanical quadrature methods
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