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Volume 34, Issue 3
Exponential Convergence of Finite-Dimensional Approximations to Linear Bond-Based Peridynamic Boundary Value Problems

Hao Wu

DOI: 10.13447/j.1674-5647.2018.03.09

Commun. Math. Res., 34 (2018), pp. 278-288.

Published online: 2019-12

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  • Abstract

In this paper, we demonstrate that the finite-dimensional approximations to the solutions of a linear bond-based peridynamic boundary value problem converge to the exact solution exponentially with the analyticity assumption of the forcing term, therefore greatly improve the convergence rate derived in literature.

  • Keywords

Peridynamics, exponential convergence, nonlocal boundary value problem, analytic function, finite-dimensional approximation

  • AMS Subject Headings

45A05, 46N20, 65B10, 65M60, 65R20

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

hzw0010@auburn.edu (Hao Wu)

  • BibTex
  • RIS
  • TXT
@Article{CMR-34-278, author = {Wu , Hao}, title = {Exponential Convergence of Finite-Dimensional Approximations to Linear Bond-Based Peridynamic Boundary Value Problems}, journal = {Communications in Mathematical Research }, year = {2019}, volume = {34}, number = {3}, pages = {278--288}, abstract = {

In this paper, we demonstrate that the finite-dimensional approximations to the solutions of a linear bond-based peridynamic boundary value problem converge to the exact solution exponentially with the analyticity assumption of the forcing term, therefore greatly improve the convergence rate derived in literature.

}, issn = {2707-8523}, doi = {https://doi.org/10.13447/j.1674-5647.2018.03.09}, url = {http://global-sci.org/intro/article_detail/cmr/13494.html} }
TY - JOUR T1 - Exponential Convergence of Finite-Dimensional Approximations to Linear Bond-Based Peridynamic Boundary Value Problems AU - Wu , Hao JO - Communications in Mathematical Research VL - 3 SP - 278 EP - 288 PY - 2019 DA - 2019/12 SN - 34 DO - http://doi.org/10.13447/j.1674-5647.2018.03.09 UR - https://global-sci.org/intro/article_detail/cmr/13494.html KW - Peridynamics, exponential convergence, nonlocal boundary value problem, analytic function, finite-dimensional approximation AB -

In this paper, we demonstrate that the finite-dimensional approximations to the solutions of a linear bond-based peridynamic boundary value problem converge to the exact solution exponentially with the analyticity assumption of the forcing term, therefore greatly improve the convergence rate derived in literature.

Wu , Hao. (2019). Exponential Convergence of Finite-Dimensional Approximations to Linear Bond-Based Peridynamic Boundary Value Problems. Communications in Mathematical Research . 34 (3). 278-288. doi:10.13447/j.1674-5647.2018.03.09
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