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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Bibliographic Details
Published in:Numerical algorithms Vol. 62; no. 1; pp. 27 - 43
Main Authors: Luo, Xin, Huang, Jin, Wang, Chuan-Long
Format: Journal Article
Language:English
Published: Boston Springer US 01.01.2013
Springer Nature B.V
Subjects:
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
Anisotropic
Mechanical quadrature methods
Darcy’s equation
A posteriori estimate
Splitting extrapolation algorithm
ISSN:1017-1398, 1572-9265
Online Access:Get full text
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Summary: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.
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ISSN:1017-1398
1572-9265
DOI:10.1007/s11075-012-9563-0