> if this is correct, my approach is slightly different, since i start from a > discrete lagrangian. that is, the 1st step has to be "discretize" - i have > already chosen my basis functions and the primal discretization is fully > determined (SIPG in my case). Then, I proceed to write the Lagrangian; > after that, the discrete optimality conditions (a discrete counterpart to > equation 2.7). then i go ahead and optimize the discrete kkt system that is > obtained through direct differentiation of my discrete "equation 2.7". can > this approach be implemented in deal.ii?
Sure. > I do not think the 1st two steps (i.e. discretization of the primal and > formulation of the lagrangian) commute in all cases; if they do, what you > are describing would probably be equivalent to what i am doing... Right. The steps don't commute if your discretization has stabilization terms, in particular if they are non-symmetric. > what approach do you suggest? I personally like the approach to leave the discretization as the last step and work in function spaces. I find that this is the most natural thing to do in the finite element method, but at least if you don't intend to change the mesh between nonlinear iterations it probably doesn't have advantages over any of the other approaches. I think there is nothing wrong with using the simplest approach in many cases; for example, if you wanted to use an external optimization package you *need* to discretize first because they want to work on finite dimensional vectors. Best W. ------------------------------------------------------------------------- Wolfgang Bangerth email: [email protected] www: http://www.math.tamu.edu/~bangerth/ _______________________________________________ dealii mailing list http://poisson.dealii.org/mailman/listinfo/dealii
