Corrected stabilized non-conforming nodal integration in meshfree methods

Marcus Rüter, Michael Hillman, Jiun Shyan Chen

Research output: Chapter in Book/Report/Conference proceedingConference contribution

8 Scopus citations

Abstract

A novel approach is presented to correct the error from numerical integration in Galerkin methods for meeting linear exactness. This approach is based on a Ritz projection of the integration error that allows a modified Galerkin discretization of the original weak form to be established in terms of assumed strains. The solution obtained by this method is the correction of the original Galerkin discretization obtained by the inaccurate numerical integration scheme. The proposed method is applied to elastic problems solved by the reproducing kernel particle method (RKPM) with first-order correction of numerical integration. In particular, stabilized non-conforming nodal integration (SNNI) is corrected using modified ansatz functions that fulfill the linear integration constraint and therefore conforming sub-domains are not needed for linear exactness. Illustrative numerical examples are also presented.

Original languageEnglish (US)
Title of host publicationMeshfree Methods for Partial Differential Equations VI
Pages75-92
Number of pages18
DOIs
StatePublished - Jan 21 2013
Event6th International Workshop on Meshfree Methods for Partial Differential Equations - Bonn, Germany
Duration: Oct 4 2011Oct 6 2011

Publication series

NameLecture Notes in Computational Science and Engineering
Volume89 LNCSE
ISSN (Print)1439-7358

Other

Other6th International Workshop on Meshfree Methods for Partial Differential Equations
CountryGermany
CityBonn
Period10/4/1110/6/11

All Science Journal Classification (ASJC) codes

  • Modeling and Simulation
  • Engineering(all)
  • Discrete Mathematics and Combinatorics
  • Control and Optimization
  • Computational Mathematics

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