How to redirect stdout and stderr to log files in a Bash script

script.sh

#!/bin/bash

script=$(basename ${0})
exec > >(tee -ia /var/log/${script}_out.log)    # Redirect stdout to logfile and continue to print on stdout
exec 2> >(tee -ia /root/${script}_err.log >&2)  # Redirect stderr to logfile and continue to print of stderr

echo stdout     # Appears on stdout and in logfile
echo stderr >&2 # Appears on stderr and in logfile