Domestic Electric Water Heaters account for a large portion of household electricity usage due to standby heat loss and varying user consumption behavior, making smart energy management strategies for these appliances increasingly important for smart home and demand-side management applications. This paper presents an energy-saving schedule and control strategy for DEWHs that incorporates user behavior patterns and insulation properties to achieve efficient energy usage without compromising user satisfaction. Transient thermodynamic models are derived by applying the first and second laws of thermodynamics to heating, standby heat losses, and disturbances caused by hot water consumption, and the proposed control and schedule framework is evaluated through simulation. Thermal resistance of the water tank is varied from 0.1 K/W to 3.0 K/W, with two typical user schedules, a family schedule and a single user schedule, used for comparison. Simulation results comparing standard thermostat control with the proposed scheduling method show energy savings of up to 51% for poorly insulated systems, where standby heat loss dominates energy waste, decreasing to around 27% as thermal resistance increases, indicating a new thermally robust operating state. These findings offer useful insights for designing smart home energy management systems and adaptive control strategies for residential water heating applications.