Generation of discretization with prescribed element sizes are adapted to the geometry. From the rules of thumb, for a complicated geometry it is important to select the reasonable element order, shapes and size for accurate results. In order to that, this paper describes the influence of elemental algorithm of the catalytic converter mounting brackets. Brackets are main source of mounting of various systems mainly intake and exhaust in the engine. In hot end exhaust system, a bracket design plays a vital role because it has to withstand heavy structural vibrations without isolation combined with thermal loads.Bracket design and stiffness determines the whole catalytic converter system's rigidity. So, here discretization of converter brackets by linear and parabolic elements is studied with different elements types and compared. The study shows disparity in the structural accuracies of the brackets in each of elemental orders respect to the element shapes i.e. in the stiffness and resonance frequencies. For an optimized proposal it is significant to predict the accurate resonances along with desired stiffness target in less time consumption. To accomplish these, a detailed perspective is given for selection of elemental orders and shapes.