Re: [Libmesh-users] error about solving darcy equation with mixed FEM

 Re: [Libmesh-users] error about solving darcy equation with mixed FEM From: Roy Stogner - 2007-09-11 04:53:08 ```On Tue, 11 Sep 2007, Shengli Xu wrote: > Hi, I use the mixed galerkin finite element to sovle darcy equation. > pressure is linear interpretation, velocity is quadratic interpretation¡£ The > domain is square. The result is correct when I apply no-slip b.c on top and > bottom side, zero pressure on right-bottom corner, Ux=1.0 on left side. But > I can not get correct result if I apply no-slip b.c on top and bottom side, > zero pressure on the right side, P=1 on the left side. Why can I get correct > result with this b.c.? Unless someone has seen a similar Darcy-flow problem before (John?), which is a long shot, you're not likely to find someone who can answer this. If you've already got the problem boiled down to a simple benchmark, I'd try running it on a single square element and comparing the numerical linear system to what you can compute by hand. Doing so for even that bare minimum (22x22 in your case, I suppose) system can be tedious, but in the past it's been the only way I've been able to find one or two subtle bugs in application codes. --- Roy```

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 [Libmesh-users] error about solving darcy equation with mixed FEM From: Shengli Xu - 2007-09-11 03:10:32 Attachments: Message as HTML ```Hi, I use the mixed galerkin finite element to sovle darcy equation. pressure is linear interpretation, velocity is quadratic interpretation。 The domain is square. The result is correct when I apply no-slip b.c on top and bottom side, zero pressure on right-bottom corner, Ux=1.0 on left side. But I can not get correct result if I apply no-slip b.c on top and bottom side, zero pressure on the right side, P=1 on the left side. Why can I get correct result with this b.c.? -- Best regards, Yours sincerely ShengliXu Department of Engineering Mechanics State Key Laboratory of Structural Analysis for Industrial Equipment Dalian University of Technology Dalian, 116023, P. R. China Email:shengli@... shengli.xu.xu@... ========================== ```
 Re: [Libmesh-users] error about solving darcy equation with mixed FEM From: Roy Stogner - 2007-09-11 04:53:08 ```On Tue, 11 Sep 2007, Shengli Xu wrote: > Hi, I use the mixed galerkin finite element to sovle darcy equation. > pressure is linear interpretation, velocity is quadratic interpretation¡£ The > domain is square. The result is correct when I apply no-slip b.c on top and > bottom side, zero pressure on right-bottom corner, Ux=1.0 on left side. But > I can not get correct result if I apply no-slip b.c on top and bottom side, > zero pressure on the right side, P=1 on the left side. Why can I get correct > result with this b.c.? Unless someone has seen a similar Darcy-flow problem before (John?), which is a long shot, you're not likely to find someone who can answer this. If you've already got the problem boiled down to a simple benchmark, I'd try running it on a single square element and comparing the numerical linear system to what you can compute by hand. Doing so for even that bare minimum (22x22 in your case, I suppose) system can be tedious, but in the past it's been the only way I've been able to find one or two subtle bugs in application codes. --- Roy```
 Re: [Libmesh-users] error about solving darcy equation with mixed FEM From: John Peterson - 2007-09-11 14:21:49 ```Isn't the Darcy velocity u ~ grad(p)=3F In that case I don't understan= d the rationale for using a higher-order approximation for velocity. Mixed methods are notorious for stability/compatibility restrictions on the pair of approximation spaces used. I'm not familiar enough with= Darcy flow to know whether the one you've chosen is LBB-stable. -John Roy Stogner writes: > On Tue, 11 Sep 2007, Shengli Xu wrote: >=20 > > Hi, I use the mixed galerkin finite element to sovle darcy equatio= n. > > pressure is linear interpretation, velocity is quadratic interpret= ation=A1=A3 The > > domain is square. The result is correct when I apply no-slip b.c o= n top and > > bottom side, zero pressure on right-bottom corner, Ux=3D1.0 on lef= t side. But > > I can not get correct result if I apply no-slip b.c on top and bot= tom side, > > zero pressure on the right side, P=3D1 on the left side. Why can I= get correct > > result with this b.c.=3F >=20 > Unless someone has seen a similar Darcy-flow problem before (John=3F= ), > which is a long shot, you're not likely to find someone who can answ= er > this. If you've already got the problem boiled down to a simple > benchmark, I'd try running it on a single square element and compari= ng > the numerical linear system to what you can compute by hand. Doing > so for even that bare minimum (22x22 in your case, I suppose) system= > can be tedious, but in the past it's been the only way I've been abl= e > to find one or two subtle bugs in application codes. > --- > Roy ```