The Cartesian grid Discontinuous Galerkin finite element method cgDG [1] is recently developed simulation tool for efficiently simulating physical phenomena governed by hyperbolic partial differential equations in the time domain. Although the NURBS-enhanced integration automatically neglects model approximation errors, the solution’s accuracy depends on the selected polynomial basis used to compute the numerical approximation. The obtention of accurate meshes becomes a time-consuming and expertise demanding task, since the analyst is responsible for generating an appropriate mesh to deal with discretisation errors, since the solution varies in time. Automated mesh adaptation algorithms require an indicator of the discretisation error in the computation mesh. In this work, we have compared the behaviour in the context of cgDG of a set of strategies used to measure the level of error due to spatial discretisation [2]. These strategies range from recovery procedures such as Richardson extrapolation or patch recovery techniques to explicit error indicators. The comparison outlined the high efficiency of explicit error indicators. Finally, our indicator has been included in an automated adaption strategy that considers refinement and coarsening of the space discretisation. A set of numerical studies highlight the ability of computing highly accurate results with minimal analyst intervention, having an initial uniform coarse mesh. REFERENCES [1] H. Navarro-García, R. Sevilla, E. Nadal, JJ. Ródenas. High-order discontinuous Galerkin method for time-domain electromagnetics on geometry-independent Cartesian meshes. Int J Numer Methods Eng. 2021; 122(24): 7632- 7663. doi:10.1002/nme.6846 [2] L. Chamoin, P. Díez. Verifying Calculations - Forty Years On: An Overview of Classification Verification Techniques for FEM Simulations. Cham, Switzerland: Springer International Publishing; 2016. Springer Briefs in Applied Sciences and Technology. ACKNOWLEDGEMENTS The authors gratefully acknowledge the financial support of the Ministry of Universities (FPU17 /03993), Generalitat Valenciana (Prometeo/2021/046) and Ministry of Science and Innovation/AEI/10.13039/501100011033/FEDER, UE (project PID2022-141512NB-I00)