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The present work explores an error analysis of Galerkin finite element method (GFEM) for computing steady heat conduction in order to show its convergence and accuracy. The steady state heat distribution in a planar region is modeled by two-dimensional Laplace partial differential equations. A simple three-node triangular finite element model is used and its derivation to form elemental stiffness matrix for unstructured and structured grid meshes is presented. The error analysis is performed bydoi:10.17485/ijst/2016/v9i36/102158 fatcat:gv5g67twlzfmxdld6utehty7aq