Trilinear Finite Element Solution of Three Dimensional Heat Conduction Partial Differential Equations

  • Authors

    • Erwin Sulaeman
    • S. M. Afzal Hoq
    • Abdurahim Okhunov
    • Marwan Badran
    2018-12-09
    https://doi.org/10.14419/ijet.v7i4.36.28146
  • Trilinear finite element method, hexahedron finite element, Galerkin method, 3D-Laplace equation, error analysis, heat conduction.

  • Abstract

    Solution of partial differential equations (PDEs) of three dimensional steady state heat conduction and its error analysis are elaborated in the present paper by using a Trilinear Galerkin Finite Element method (TGFEM). An eight-node hexahedron element model is developed for the TGFEM based on a trilinear basis function where physical domain is meshed by structured grid.  The stiffness matrix of the hexahedron element is formulated by using a direct integration scheme without the necessity to use the Jacobian matrix.  To check the accuracy of the established scheme, comparisons of the results using error analysis between the present TGFEM and exact solution is conducted for various number of the elements.  For this purpose, analytical solution is derived in detailed for a particular heat conduction problem.  The comparison shows promising result where its convergence is approximately O(h²) for matrix norms L1, L2 and L¥.

     

     

  • References

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  • How to Cite

    Sulaeman, E., M. Afzal Hoq, S., Okhunov, A., & Badran, M. (2018). Trilinear Finite Element Solution of Three Dimensional Heat Conduction Partial Differential Equations. International Journal of Engineering & Technology, 7(4.36), 379-384. https://doi.org/10.14419/ijet.v7i4.36.28146

    Received date: 2019-03-03

    Accepted date: 2019-03-03

    Published date: 2018-12-09