One of the major challenges in wide use of Grid workflow systems is fault tolerance and avoidance. Checkpointing schemes provide a way of fault detection and recovery. In our research, we focus on performance optimization of checkpointing schemes and DVS (Dynamic Voltage Scaling) for Grid workflow systems. We propose offline checkpointing schemes with DVS and online adaptive checkpointing schemes that dynamically adjust the checkpointing intervals by using store-checkpoints (SCPs) and compare-checkpoints (CCPs). When combined with DVS, offline adaptive checkpointing schemes not only are fault tolerant but also lead to reduce average execution time of tasks. These schemes can efficiently utilize comparison and storage operations and significantly improve the performance. Further, these schemes can calculate the optimal numbers of checkpoints by which minimize the mean execution time. We also expand the online adaptive checkpointing schemes from single-task execution scenarios to multi-task execution scenarios. Simulation results show these online schemes outstandingly increase the likelihood of timely task completion when faults occur.