Imposition of the essential boundary conditions in transient heat conduction problem based on Isogeometric analysis

The purpose of this paper is using the proposed two step method to impose essential boundary conditions for improving the accuracy of solution field. In the proposed approach, imposing essential boundary conditions in transient heat flow within two-dimensional region is extended in two steps. The essential boundary conditions are defined on Dirichlet boundary as determined temperatures and independent of time. In the first step, Dirichlet boundary conditions are weakly built into the variational formulation, choosing weight function, appropriately. In the second step, with fixed condition, the system of equations is appropriately adjusted. For investigation of the efficiency of the proposed approach, several 2D numerical examples have been performed. The results demonstrate significant improvement in accuracy and rate of convergence in comparison with direct imposition of essential boundary condition.