Convergence and error analysis of a bi-quadratic triangular galerkin finite element model for heat conduction simulation

Present paper elaborates solution of partial differential equations (PDE) of two dimensional steady state heat conduction by using a bi quadratic triangular Galerkin's finite element method (QGFEM). The steady state heat distribution is modeled by a two-dimensional Laplace partial differential equations. A six- point triangular planar finite element model is developed for the QGFEM based on quadratic basis functions on the Cartesian coordinate system where physical domain is meshed by structured grid. The elemental stiffness matrix is formulated by using a direct integration scheme along the trilateral domain area without the necessity to use the Jacobian matrix. Validation is conducted to an analytical solution of a rectangular plate having mixed, asymmetric boundary conditions. Comparisons of the present QGFEM results and the exact solution show promising results. The convergence of the method is presented by checking the error analysis for various number of elements used for the simulation.