Titus 2:11 is the elect. Paul was writing to them who had the faith of God's Elect
Titus 1:1
Paul, a servant of God, and an apostle of Jesus Christ, according to the faith of God's elect, and the acknowledging of the truth which is after godliness;
God's Elect are the ones who hear the Gospel being convicted of sin and seeing a need for a Savior, and believing, accepting the call.