A Lagrangian uniform-mesh finite element method applied to problems governed by Poisson's Equation

Linxia Gu, Ashok V. Kumar

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

Abstract

A method is presented for the solution of Poisson's Equations using a Lagrangian formulation. The interpolation functions are the Lagrangian operation of those used in the classical finite element method, which automatically satisfy boundary conditions exactly even though there are no nodes on the boundaries of the domain. The integration is introduced in an implicit way by using approximated step functions. Classical surface integration terms used in the weak form are unnecessary due to the interpolation function in the Lagrangian formulation. Furthermore, the Lagrangian formulation simplified the connection between the mesh and the solid structures, thus providing a very easy way to solve the problems without a conforming mesh.

Original languageEnglish (US)
Title of host publicationProceedings of the ASME International Mechanical Engineering Congress and Exposition, IMECE 2007
Pages129-138
Number of pages10
DOIs
StatePublished - Jun 2 2008
EventASME International Mechanical Engineering Congress and Exposition, IMECE 2007 - Seattle, WA, United States
Duration: Nov 11 2007Nov 15 2007

Publication series

NameASME International Mechanical Engineering Congress and Exposition, Proceedings
Volume8 PART A

Conference

ConferenceASME International Mechanical Engineering Congress and Exposition, IMECE 2007
CountryUnited States
CitySeattle, WA
Period11/11/0711/15/07

Fingerprint

Poisson equation
Finite element method
Interpolation
Boundary conditions

Keywords

  • Implicit solid
  • Lagrangian formulation
  • Step function
  • Uniform mesh

ASJC Scopus subject areas

  • Engineering(all)
  • Mechanical Engineering

Cite this

Gu, L., & Kumar, A. V. (2008). A Lagrangian uniform-mesh finite element method applied to problems governed by Poisson's Equation. In Proceedings of the ASME International Mechanical Engineering Congress and Exposition, IMECE 2007 (pp. 129-138). (ASME International Mechanical Engineering Congress and Exposition, Proceedings; Vol. 8 PART A). https://doi.org/10.1115/IMECE2007-41282

A Lagrangian uniform-mesh finite element method applied to problems governed by Poisson's Equation. / Gu, Linxia; Kumar, Ashok V.

Proceedings of the ASME International Mechanical Engineering Congress and Exposition, IMECE 2007. 2008. p. 129-138 (ASME International Mechanical Engineering Congress and Exposition, Proceedings; Vol. 8 PART A).

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

Gu, L & Kumar, AV 2008, A Lagrangian uniform-mesh finite element method applied to problems governed by Poisson's Equation. in Proceedings of the ASME International Mechanical Engineering Congress and Exposition, IMECE 2007. ASME International Mechanical Engineering Congress and Exposition, Proceedings, vol. 8 PART A, pp. 129-138, ASME International Mechanical Engineering Congress and Exposition, IMECE 2007, Seattle, WA, United States, 11/11/07. https://doi.org/10.1115/IMECE2007-41282
Gu L, Kumar AV. A Lagrangian uniform-mesh finite element method applied to problems governed by Poisson's Equation. In Proceedings of the ASME International Mechanical Engineering Congress and Exposition, IMECE 2007. 2008. p. 129-138. (ASME International Mechanical Engineering Congress and Exposition, Proceedings). https://doi.org/10.1115/IMECE2007-41282
Gu, Linxia ; Kumar, Ashok V. / A Lagrangian uniform-mesh finite element method applied to problems governed by Poisson's Equation. Proceedings of the ASME International Mechanical Engineering Congress and Exposition, IMECE 2007. 2008. pp. 129-138 (ASME International Mechanical Engineering Congress and Exposition, Proceedings).
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