## Re: [Libmesh-users] mathematic help

 Re: [Libmesh-users] mathematic help From: Roy Stogner - 2007-04-22 13:14:32 ```On Sun, 22 Apr 2007, li pan wrote: > I have mathematic problem which I thought long time. > I'm not a mathematician and the people around me can > not help me either. I hope any mathematic experts can > give some advice. > The question is: how to discretise > grad(div(u)) with Galerkin method? Well, I think by the definition of Galerkin the discretization will be: (grad(div(u)), v) Which you'll normally integrate by parts out to: (div(u), div(v)) plus boundary terms. Unless this is a relatively unimportant term in a larger problem, though, trying to solve equations based on this will give you some trouble. Notice that you can add any divergence-free vector field to u, or any compactly-supported divergence-free field to v, without changing the value of the bilinear form. So if you're just trying to solve something like "grad(div(u)) = f", you'll have a singular system (and depending on curl(f), possibly an insoluble system) on your hands. --- Roy ```

 [Libmesh-users] mathematic help From: li pan - 2007-04-22 09:43:41 ```Hello, I have mathematic problem which I thought long time. I'm not a mathematician and the people around me can not help me either. I hope any mathematic experts can give some advice. The question is: how to discretise grad(div(u)) with Galerkin method? pan __________________________________________________ Do You Yahoo!? Tired of spam? Yahoo! Mail has the best spam protection around http://mail.yahoo.com ```
 Re: [Libmesh-users] mathematic help From: Roy Stogner - 2007-04-22 13:14:32 ```On Sun, 22 Apr 2007, li pan wrote: > I have mathematic problem which I thought long time. > I'm not a mathematician and the people around me can > not help me either. I hope any mathematic experts can > give some advice. > The question is: how to discretise > grad(div(u)) with Galerkin method? Well, I think by the definition of Galerkin the discretization will be: (grad(div(u)), v) Which you'll normally integrate by parts out to: (div(u), div(v)) plus boundary terms. Unless this is a relatively unimportant term in a larger problem, though, trying to solve equations based on this will give you some trouble. Notice that you can add any divergence-free vector field to u, or any compactly-supported divergence-free field to v, without changing the value of the bilinear form. So if you're just trying to solve something like "grad(div(u)) = f", you'll have a singular system (and depending on curl(f), possibly an insoluble system) on your hands. --- Roy ```