NURBS-based isogeometric analysis of two-dimensional linear convection-diffusion problems

NURBS-based isogeometric analysis method provides an effective integration between the CAGD and the finite element analysis. In this paper, the isogeometric analysis method is applied to two-dimensional linear convection-diffusion problems. First, a new stable and discrete solution is proposed by combining the SUPG (streamline upwind Petrov-Galerkin) method and the isogeometric analysis method, and thus, the discrete stable format of isogeometric solution is established. Then time domain is discretized by the θ weighting method to get the final isogeometric solution form which is fully discrete. At the same time, to reduce the essential boundary handling error caused by non-interpolation of NURBS basis function, the penalty function is introduced. Finally, two numerical examples are presented to prove the effectiveness of the approach.