Finite element analysis of transient heat conduction application of the weighted residual process

The transient heat conduction problem can be solved by application of Galerkin's method to space as well as time discretization. The formulation corresponds to the procedure known as finite elements in time and space. A linear time expansion leads to a step by step technique which is convergent, consistent and absolutely stable. Several numerical examples are presented using two-dimensional isoparametric elements.