Feel free to put your wishes and questions into this file. It would be nice to prefix your statements with your initials or one more letter if needed.

• OS: How do I specialize code for a particular basis? For example, how can I write an 'interpolate' method only for BSPlineBasis objects?

Development

Function space basis interface

• Here is another point that needs future discussion: I just added the first implementation of a basis of a DG space. This one uses Lagrangian shape functions. I expect other DG spaces using other shape functions to appear eventually. Here is the issue: Currently, the LagrangeDGBasis has the shape function type hard-wired into the code. Any implementation for a DG space using a different set of shape functions will differ very little from it. Hence one may consider implementing a single DGBasis, and making the shape functions a template parameter. However, it is not clear what exactly this template parameter should be. It cannot be a LocalFiniteElement, because that would force us to pick a grid element type at compile time (you currently could not use the VirtualLocalFiniteElement here, because the code does not properly set it up). You cannot expect a factory here either, because then you cannot currently hard-wire the element type if that is what you want. I don't think this is a difficult issue, it just needs a bit of discussion.

Function interface

EntitySet interface

• CaG: It seems that the EntitySet concept and GridViewEntitySet are candidates for dune-grid.

GridFunction concept

• CaG: Should GridFunction export the grid type?
• CaG: If yes, should GridFunction store/export a pointer to the grid?
• CaG: While LocalFunction is defined in a grid-agnostig way with local coordinates from a 'LocalContext'. In contrast to this the naming of GridFunction is linked to Grids: entitySet(), LocalContext=decltype(entitySet())::Element. There seems to be no need for this and we could simply rename this in a grid-agnostic way if someone comes up with better names than LocalizableFunction, localContextSet()