Just to clarify for others as I've stumbled on this question when first searching for it on Google:
Issue: After doing all the necessary setup for a LUKS container file/harddisk that is already mounted with root, a user account has not write privileges to it, only read. (this is the case for most tutorials and instructions above)
We need to change the permissions of the newly-minted filesystem that is in the encrypted harddisk/file container.
Using the example in the example where
/dev/mapper/$name has already been mounted to
/media/mount_point with a command like:
sudo mount /dev/mapper/$name /media/mount_point
Open a terminal in your account and type enter this command:
sudo chown -R yourUserName /media/mount_point
For example if joe has a mount point named myEncryptedHD he should do:
sudo chown -R joe /media/myEncryptedHD
What this does is Joe changes the owner of all files in
joe, and he now has read and write access. Life is good.
If you decide you don't want R/W permissions anymore, just
sudo chown -R root /media/mount_point and you'll revoke your rights.
References for chown examples for more complicated permissions handling and a related question on SuperUser with a comment on the answer that also suggests the alternative
sudo chmod -R 775 /media/mount_point that will set read write execute permissions on user, group and only read and execute (5) for others. A chmod man page for further info