A 74-year-old woman with severe chronic obstructive pulmonary disease presents with increasing dyspnoea and drowsiness during a respiratory infection. On room air her oxygen saturation is 82%. She has peripheral cyanosis but no stridor, and her blood pressure is 138/76 mmHg. Previous records show a stable PaCO2 of about 60 mmHg. Which one of the following is the most appropriate initial oxygen treatment while investigations and bronchodilator therapy are arranged?