Step-20 tutorial says that: *"It turns out that the usual discretizations of the Laplace equation (such as those used in step-3 <https://dealii.org/developer/doxygen/deal.II/step_3.html>, step-4 <https://dealii.org/developer/doxygen/deal.II/step_4.html>, or step-6 <https://dealii.org/developer/doxygen/deal.II/step_6.html>) do not satisfy a desirable feature in typical porous media applications, i.e. that the numerical scheme is locally conservative, implying that whatever flows into a cell also flows out of it (or the difference is equal to the integral over the source terms over each cell, if the sources are nonzero). But, one can achieve this by choosing a different formulation of the problem and a particular combination of finite element spaces."*
Those arriving at the step-20 tutorial from step-6 (following the video lectures) can be taken by surprise by the above statement (since this may be a big jump in concepts to be understood). I know that this is not the responsibility of the library to impart the theoretical knowledge, but among the user community here, can someone point to a quick reference to a webpage or lecture slides that mathematically shows that the standard discretizations are not locally conservative while the proposed replacement scheme is? Regards, Krishna -- The deal.II project is located at http://www.dealii.org/ For mailing list/forum options, see https://groups.google.com/d/forum/dealii?hl=en --- You received this message because you are subscribed to the Google Groups "deal.II User Group" group. To unsubscribe from this group and stop receiving emails from it, send an email to dealii+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/dealii/37e27105-8ac1-4361-abda-023e2652ac17%40googlegroups.com.
