tee stdout and stderr to separate files while retaining them on their respective streams

A process-substitution-based solution is simple, although not as simple as you might think. My first attempt seemed like it should work

{ echo stdout; echo stderr >&2; } > >( tee ~/stdout.txt ) \                                 2> >( tee ~/stderr.txt )

However, it doesn't quite work as intended in bash because the second tee inherits its standard output from the original command (and hence it goes to the first tee) rather than from the calling shell. It's not clear if this should be considered a bug in bash.

It can be fixed by separating the output redirections into two separate commands:

{ { echo stdout; echo stderr >&2; } > >(tee stdout.txt ); } \                                   2> >(tee stderr.txt )

Update: the second tee should actually be tee stderr.txt >&2 so that what was read from standard error is printed back onto standard error.

Now, the redirection of standard error occurs in a command which does not have its standard output redirected, so it works in the intended fashion. The outer compound command has its standard error redirected to the outer tee, with its standard output left on the terminal. The inner compound command inherits its standard error from the outer (and so it also goes to the outer tee, while its standard output is redirected to the inner tee.