In general with Adobe software, newer versions of a program can open/import project files created with older versions. This makes sense, since it would be pretty stupid if you couldn't open your old projects anymore after upgrading your software version. However, in most cases the project files are not backwards compatible, meaning you can't open a project created with the current version of your software with an older release of the same software.
For this reason, if you open an old project file with a newer release of Premiere Pro, it informs you that the project file needs to be converted and prompts you to save the new project file with a new name. This way, you will still have the old project file that can be opened with the older version of Premiere. However, any additional changes you make to the project will only be present in the converted project.
For Elements, I'm not sure how the conversion is handled, but you will definitely be able to open your Premiere Elements 11 project file with Premiere Elements 15. However, once you overwrite the project file from within Premiere Elements 15, you probably won't be able to open it in Premiere Elements 11 anymore.