Paper Info
Title
Tailored finite point method for the interface problem
Abstract
In this paper, we propose a tailored-finite-point method for a numerical simulation of the second order elliptic equation with discontinuous coefficients. Our finite point method has been tailored to some particular properties of the problem, then we can get the approximate solution with the same behaviors as that of the exact solution very naturally. Especially, in one-dimensional case, when the coefficients are piecewise linear functions, we can get the exact solution with only one point in each subdomain. Furthermore, the stability analysis and the uniform convergence analysis in the energy norm are proved. On the other hand, our computational complexity is only O(N) for N discrete points. We also extend our method to two-dimensional problems.
Year
DOI
Venue
2009
10.3934/nhm.2009.4.91
NETWORKS AND HETEROGENEOUS MEDIA
Keywords
Field
DocType
Tailored finite point method,interface problem,elliptic equation,discontinuous coefficients,jump conditions
Exact solutions in general relativity,Mathematical optimization,Discrete points,Mathematical analysis,Uniform convergence,Finite point method,Approximate solution,Mathematics,Piecewise,Elliptic curve,Computational complexity theory
Journal
Volume
Issue
ISSN
4
1
1556-1801
Citations 
PageRank 
References 
4
0.84
4
Authors
1
Name
Order
Citations
PageRank
Zhongyi Huang16712.67