期刊
SIAM JOURNAL ON NUMERICAL ANALYSIS
卷 51, 期 2, 页码 1211-1234出版社
SIAM PUBLICATIONS
DOI: 10.1137/120871638
关键词
nonlocal diffusion; peridynamics; adaptive finite element method; a posteriori error estimation; convergence; fractional Sobolev space
资金
- U.S. Department of Energy [DE-SC0005346]
- U.S. NSF [DMS-1016073]
- National Nature Science Foundation of China [11201462]
- China Postdoctoral Science Foundation [20110490279]
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [1016073] Funding Source: National Science Foundation
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 delta which characterizes the range of nonlocality. Numerical experiments are performed to verify our theoretical findings.
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