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A Conforming DG Method for Linear Nonlocal Models with Integrable Kernels

  • Qiang Du
  • Xiaobo YinEmail author
Article
  • 1 Downloads

Abstract

The numerical solution of nonlocal constrained value problems with integrable kernels is considered. These nonlocal problems arise in nonlocal mechanics and nonlocal diffusion. The structure of the true solution to the problem is analyzed first. The analysis leads naturally to a new kind of discontinuous Galerkin method that can more efficiently solve the problem numerically. The new method is shown to be asymptotically compatible. Moreover, it has optimal convergence rate for any dimensional case under mild assumptions.

Keywords

Nonlocal diffusion Peridynamic model Nonlocal model Integrable kernel Discontinuous Galerkin Finite element Convergence analysis Condition number 

Mathematics Subject Classification

82C21 65R20 74S05 46N20 45A05 

Notes

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Applied Physics and Applied MathematicsColumbia UniversityNew YorkUSA
  2. 2.Hubei Key Laboratory of Mathematical Sciences & School of Mathematics and StatisticsCentral China Normal UniversityWuhanChina

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