Compatibility between Dell UltraSharp U2715H monitor and 2011 non-retina 13" Macbook Pro
Your model MacBook Pro shipped with an onboard Intel HD Graphics 3000 graphics card. This graphics card uses a minimum of 384 MB of DDR3 SDRAM shared with your main memory (i.e. your computer's RAM). The amount of memory it actually uses will vary depending on your graphics needs. 

In terms of connecting an external display, your computer has a Thunderbolt digital video output port and supports the following display modes:


Dual display extended
Video mirroring
AirPlay Mirroring (not relevant in your scenario)


Your MacBook Pro supports an external resolution up to 2560 x 1600 pixels.

As for the Dell UltraSharp U2715H this has an optimal resolution of 2560 x 1440 pixels at 60Hz.

In terms of your concern relating to black rectangles and aspect ratios, this will depend on how you use it? Do you intend to extend your display or mirror it?

Regardless, this monitor uses a 16:9 aspect ratio and your MacBook Pro supports the following resolutions at the 16:10 aspect ratio (that you can mirror):


1280 x 800 (native)
1152 x 720
1024 x 640
800 x 500 


Whether the difference between 16:10 and 16:9 will annoy you, only you can answer.

However, if you want to use it in dual display extended mode (I'm guessing you do), then you would just take advantage of the best resolution your MBP can output to the monitor.

The only hesitation I would have (and this would apply to any external display) is that you haven't specified how much RAM you have, so if you intend to do anything that is graphics heavy on the external display, you may find the Intel HD Graphics 3000 graphics card struggling.

Otherwise you should be happy with this display (if you really need the 27").

[EDIT]

(Additional info re screens with DVI ports)

If you go ahead with a different external display requiring a DVI connection and find that the highest available resolution is 1280 x 800 instead of 2560 x 1600, this is likely due to you using a single-link DVI connection on a display that requires a dual-link DVI connection. (Note: This is not a factor for the U2715H you're looking at, but may be for others).

If this happens you would need to connect the display to a dual-link DVI port to access the higher resolutions available. However, your model MacBook Pro does not provide a dual-link DVI connection without an appropriate adaptor!

For best results you will need to use a Mini DisplayPort to Dual-Link DVI adapter.

You should refer to this info on Apple's website (as the general info is still applicable to many external displays). Also of interest may be this Mini DisplayPort adapter FAQs page.