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A Lagrangian Uniform-Mesh Finite Element Method Applied to Problems Governed by Poisson’s Equation

[+] Author Affiliations
Linxia Gu

South Dakota School of Mines and Technology, Rapid City, SD

Ashok V. Kumar

University of Florida, Gainesville, FL

Paper No. IMECE2007-41282, pp. 129-138; 10 pages
  • ASME 2007 International Mechanical Engineering Congress and Exposition
  • Volume 8: Heat Transfer, Fluid Flows, and Thermal Systems, Parts A and B
  • Seattle, Washington, USA, November 11–15, 2007
  • Conference Sponsors: ASME
  • ISBN: 0-7918-4302-5 | eISBN: 0-7918-3812-9
  • Copyright © 2007 by ASME


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.

Copyright © 2007 by ASME



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