Among the numerical methods in solution of engineering problems, the finite element method has a special position in computational mechanics. Due to the need for economical solution of complex problems with desirable accuracy, the so called “ Adaptive Analysis” has so far received a considerable attension by pioneering researchers. The most significant step in an adaptive analysis is estimation of the error level in the finite element solution. The quality assessment of error estimators, in order to choose the right ones for the problem of interest, plays an important role in efficiency of any adaptive solution. Comparing error estimators based on a series of benchmark problems has been a commonly accepted approach, but Babuskaand hi co-workers, in a series of papers published from 1994 to 1997 stated that benchmarking can lead to unrealistic or contradictory results. In the same publicatio the authors introduced a numerical robustness patch test suitable for assessment of asymptotic behavior of error estimators in 2D problems. The introduced patch test can only be used for patches located at interior parts of the domain, i.e. far from boundaries, as well as those located near a flat boundary. In this thesis, the patch test introduced by Babuska and co-workers is applied to recovery based error estimates using two recovery methods, i.e. Superconvergent Patch Recovery (SPR) and recovery by Equilibrium in patches (REP) in both original and improved forms. The recovery methods have been shown to be asymptotically robust and superconvergent when applied to 2D problems. In this thesis the studies are performed on 3D heat-transfer and elasticity problems with different boundary conditions, mesh patterns and aspect ratios. Additionally, the formulation used in robustness patch test has been extended to more general cases of patch locations in 3D problems. This has been performed by finding an asymptotic finite element solution near kinked boundaries irrespective of other boundary conditions at far ends of the domain. The tests are performed for patches in the middle of the domain as well as those located at flat and kinked boundaries. The test results show that, for almost all patterns considered, both recovery methods exibite full superconvergent and robust behavior when the patches are located inside the domain. In addition, the original form of REP is very sensitive to high aspect ratios, and hence must not be used in problems with highly distorted mesh. Moreover, the robustness of error estimators in heat transfer problems is more than elasticity problems and also in 2D problems than 3D ones. It is observed that for special patch patterns located near boundaries, the superconvergent behavior is slightly deteriorated for both recoveries.