Finite block Petrov–Galerkin method in transient heat conduction

Based on the two-dimensional Lagrange series interpolation, the formulation of the Finite Block Petrov–Galerkin (FBPG) in the weak form is presented in this paper. In this case, the first order of partial differentials are only needed in the weak form governing equations and in the Neumann boundary condition. By introducing the mapping technique, a block of quadratic type is transformed from the Cartesian coordinate (xoy)(xoy) to the normalized coordinate (ξoη)(ξoη) with 8 seeds. Time dependent partial differential equations are analyzed in the Laplace transformed domain and the Durbin׳s inversion method is used to determine all the physical values in the time domain. Illustrative numerical examples are given and comparisons have been made with either analytical solutions or other numerical solutions including meshless method and the Finite Element Method (ABAQUS).