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 imposeessential boundary conditions for improving the accuracy of the solution eld. in theproposed approach, imposing essential boundary conditions in transient heat ow withina two-dimensional region is extended in two steps. the essential boundary conditionsare dened on the dirichlet boundary as determined temperatures and independent oftime. in the rst step, dirichlet boundary conditions are weakly built into the variationalformulation, choosing the weight function appropriately. in the second step, with a xedcondition, the system of equations is appropriately adjusted. for investigation of theeciency of the proposed approach, several 2d numerical examples have been performed.the results demonstrate signicant improvement in the accuracy and rates of convergencein comparison with direct imposition of essential boundary conditions.