deal.II uses option (2) for a long time already with very good success. In other words, in 2d, every vertex appears 4 times in the output file which means there is more data to be written but fields can be discontinuous. The only other drawback I am aware of is that some visualization programs can't follow interfaces between cells that don't share vertices when doing streamlines, though today they seem to have become better.

You may also want to look at this entry in our FAQs: http://dealii.sourceforge.net/index.php/Deal.II_Questions_and_Answers#The_graphical_output_files_don.27t_make_sense_to_me_.E2.80.94_they_seem_to_have_too_many_degrees_of_freedom.21

deal.II uses option (2) for a long time already with very good success. In other words, in 2d, every vertex appears 4 times in the output file which means there is more data to be written but fields can be discontinuous. The only other drawback I am aware of is that some visualization programs can't follow interfaces between cells that don't share vertices when doing streamlines, though today they seem to have become better.

You may also want to look at this entry in our FAQs: http://dealii.sourceforge.net/index.php/Deal.II_Questions_and_Answers#The_graphical_output_files_don.27t_make_sense_to_me_.E2.80.94_they_seem_to_have_too_many_degrees_of_freedom.21

Update: May 31, 2018

The link has been moved to: https://github.com/dealii/dealii/wiki/Frequently-Asked-Questions#the-graphical-output-files-dont-make-sense-to-me----they-seem-to-have-too-many-degrees-of-freedom