Discussion Forum

My initial question was how to solve for a system that involves a constraint on the solution variables (referred to as a differential-algebraic equation, DAE).

The set of equations I was trying to solve were 3 coupled, time-dependent pdes defining (nx, ny and nz) subject to a constraint equation, nx^2 + ny^2 + nz^2 = 1 (the DAE). This system can be rewritten in terms of a lagrange multiplier, lambda by adding the additional term lambda*nj to the source term of the corresponding equation, j. The trick to solving this sort of problem is to define the lagrange multiplier equation off of one of the other equations. For instance describing the lambda equation off of the nx pde by placing the entire equation into the source term, F. And then inserting a higher order derivative of the constraint into the equation specifying nx, in my case I used gamma = -nx*nxx and F=d(ny*nyx+nz*nzx,x) for a 1d case.

Additionally, I encountered some rather frustrating errors saying that an initial value could not be found for a well-posed system. This problem was circumvented using higher order elements.

Best of luck.


Mike