LAUSR

In this paper, a high order method using bivariate spline finite elements on domains defined by NURBS is proposed for solving two dimensional non-classical diffusion problem. Bivariate spline proper subspace of $$S_4^{2,3} (\Delta _{mn}^{(2)} )$$S42,3(Δmn(2)) satisfying homogeneous boundary conditions on type-2 triangulations and quadratic B-spline interpolating boundary functions are primarily constructed. Two examples are solved to assess the accuracy of the method. The simulation obtained, indicates that spline method is reliable and yields results compatible with the exact solutions and consistent with other existing numerical methods.