Using splines on triangular mesh to solve PDE with nonhomogeneous boundary

The spline spaces S,02(Δ(2)mn) defined on type Ⅱ regular triangulation are directly used to solve the PDE problems with homogeneous boundary.For the PDE problems with nonhomogeneous boundary, the solutions obtained usually do not satisfy the convergence properties if they are still solved in the spline spaces S,02(Δ(2)mn),because the basis functions of S,02(Δ(2)mn) vanish on the boundary of the parameter domain. Here, based on the spline spaces S,02(Δ(2)mn) and S2(Δ(2)mn) defined on type Ⅱ regular triangulation,a set of blended spline basis functions were formed by combining the basis functions of S,02(Δ(2)mn) with the basis functions of S2(Δ(2)mn) whose support centers are all outside the boundary of the parameter domain.The blended spline functions were used to solve the PDE problem with nonhomogeneous boundary.Experiment results show that the solutions obtained by this method are convergent.