How do I write stderr to a file while using “tee” with a pipe?

Question

I know how to use tee to write the output (STDOUT) of aaa.sh to bbb.out, while still displaying it in the terminal:

Answer 1

To redirect stderr to a file, display stdout to screen, and also save stdout to a file:

./aaa.sh 2>ccc.out | tee ./bbb.out

EDIT: To display both stderr and stdout to screen and also save both to a file, you can use bash's I/O redirection:

#!/bin/bash

# Create a new file descriptor 4, pointed at the file
# which will receive stderr.
exec 4<>ccc.out

# Also print the contents of this file to screen.
tail -f ccc.out &

# Run the command; tee stdout as normal, and send stderr
# to our file descriptor 4.
./aaa.sh 2>&4 | tee bbb.out

# Clean up: Close file descriptor 4 and kill tail -f.
exec 4>&-
kill %1