Processing of stderr without merging it with stdout

exp.sh

#!/bin/bash

# prepare queues
d=$(mktemp -d)
o="$d/out"
e="$d/err"
mkfifo "$o"
mkfifo "$e"

# cat the queues to outputs
cat "$o"&
outpid=$!
cat "$e" | sed 's#^#[err] #'> /dev/stderr& # you can process the output through pipe…
errpid=$!

# run the command
(echo a > /dev/stdout; echo b > /dev/stderr) > "$o" 2> "$e"

# wait for the outputters
wait $outpid $errpid

# clean it up
rm -r "$d"