Imposition of essential boundary conditions in a transient heat conduction problem based on isogeometric analysis

The purpose of this paper is the use of a proposed two-step method to impose essential boundary conditions for improving the accuracy of the solution eld. In the proposed approach, imposing essential boundary conditions in transient heat ow within a two-dimensional region is extended in two steps. The essential boundary conditions are dened on the Dirichlet boundary as determined temperatures and independent of time. In the rst step, Dirichlet boundary conditions are weakly built into the variational formulation, choosing the weight function appropriately. In the second step, with a xed condition, the system of equations is appropriately adjusted. For investigation of the eciency of the proposed approach, several 2D numerical examples have been performed. The results demonstrate signicant improvement in the accuracy and rates of convergence in comparison with direct imposition of essential boundary conditions.