an easy way is to redirect form submitter
// when form is submitted :
wp_redirect($your_post_url . '&submitform=1');
exit;
Then you can just test if “submitform” is defined to display what you want :
// test submitform url setting :
if (isset($_GET['submitform']))
echo '<div class="successmessage"><p>' . __('Your Success message.') . '</p></div>';
endif;