A CONVERGENT ADAPTIVE FINITE ELEMENT ALGORITHM FOR NONLOCAL DIFFUSION AND PERIDYNAMIC MODELS

In this paper, we propose an adaptive finite element algorithm for the numerical solution of a class of nonlocal models which correspond to nonlocal diffusion equations and linear scalar peridynamic models with certain nonintegrable kernel functions. The convergence of the adaptive finite element al...

Celý popis

Uloženo v:
Podrobná bibliografie
Vydáno v:SIAM journal on numerical analysis Ročník 51; číslo 2; s. 1211 - 1234
Hlavní autoři: DU, QIANG, TIAN, LI, ZHAO, XUYING
Médium: Journal Article
Jazyk:angličtina
Vydáno: Philadelphia Society for Industrial and Applied Mathematics 01.01.2013
Témata:
A posteriori knowledge
Adaptive algorithms
Algorithms
Applied mathematics
Approximation
Computational mathematics
Convergence
Diffusion
Estimates
Estimators
Finite element method
Interpolation
Kernel functions
Line segments
Mathematical analysis
Mathematical functions
Mathematical models
Mathematical problems
Neighborhoods
Science
Sobolev spaces
Triangles
ISSN:0036-1429, 1095-7170
On-line přístup:Získat plný text
Tagy: Přidat tag
Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!
Popis
Shrnutí:In this paper, we propose an adaptive finite element algorithm for the numerical solution of a class of nonlocal models which correspond to nonlocal diffusion equations and linear scalar peridynamic models with certain nonintegrable kernel functions. The convergence of the adaptive finite element algorithm is rigorously derived with the help of several basic ingredients, such as the upper bound of the estimator, the estimator reduction, and the orthogonality property. We also consider how the results are affected by the horizon parameter δ which characterizes the range of nonlocality. Numerical experiments are performed to verify our theoretical findings.
Bibliografie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ObjectType-Article-2
ObjectType-Feature-1
content type line 23
ISSN:0036-1429
1095-7170
DOI:10.1137/120871638