Trilinear finite element solution of three dimensional heat conduction partial differential equations - Sulaeman, Erwin; Hoq, S.M. Afzal; Okhunov, Abdurahim; Badran, Marwan A A (Science Publishing Corporation, 2018)
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.