Abstarct: Error estimation and adaptive solution of two dimensional problems with finite element as well as isogeometric analysis is dealt with in this thesis. In the finite element method an academic FORTRAN code has been developed that is able to estimate the solution error in two dimensional problems which employs the superconvergent patch stress recovery technique. Also, in order to improve the quality of the finite element solution an adaptive approach is adopted. To evaluate the accuracy of the developed code, the problem of finding the stress intensity factor in a cracked plate under tensile stresses is solved and the obtained results are compared with the analytical solution and the ANSYS commercial software. It is shown that the employed algorithm has a better performance than the algorithm used in ANSYS software and can be used for determination of the stress intensity factor in complex structures with arbitrary cracks. In addition, a new approach, baxsed on the isogeometrical analysis concept, is suggested for improvement of stresses and error estimation which falls in the category of the stress recovery error estimators. In this method, by making use of the superconvergent points, each of the components of the improved stress tensor is considered as an imaginary surface. This surface is generated by using the same NURBS’ basis functions which are employed for approximation of the primary variable in the isogeometrical analysis. The performance of the method is demonstrated by comparison of the exact and approximate energy error norms for a couple of examples that the exact solution is available for them. It seems that the suggested method can be used as a suitable approach for error estimation in the isogeometrical analysis method.