This thesis presents a comprehensive study on the dynamic analysis of crack growth, with a focus on improving the accuracy of predicting stress intensity factors, crack tip velocity, and related parameters. It introduces some strategies to appropriately model crack propagation under dynamic loading conditions and mitigate numerical oscillations that commonly affect computational results. In the pursuit of more precise time integration methods, the study employs the Discontinuous Galerkin method, which proves to be superior to traditional approaches like the Newmark method. This choice is justified by the Discontinuous Galerkin method's ability to handle discontinuities in variables over time, aligning with the dynamic nature of crack growth analysis.