http://gaia.iwr.uni-heidelberg.de/~deal/5.0.0/tutorial/chapter-2.step-by-step/step-8.html

In real life, most partial differential equations are really systems of equations. Accordingly, the solutions are usually vector-valued. The deal.II library supports such problems, and we will show that that is mostly rather simple. The only more complicated problems are in assembling matrix and right hand side, but these are easily understood as well.