Modelpde with no stabilization

Numerical methods and mathematical models of Elmer
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spacedout
Posts: 177
Joined: 30 Mar 2020, 23:27
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Modelpde with no stabilization

Post by spacedout »

Hi

I decided to use Modelpde.F90 as a template for both the Poisson and the continuity equations in my plasma research. Now, from an earlier post on June 1 2021 concerning Modelpde , I was told Stabilize is not available but that Bubble stabilization is. However because I get

ERROR:: ElementInfo: Bubbles for element: 706 are not implemented

as I reported on Nov 11 2021, I decided not to use Bubbles.

Which means that both keywords Stabilize and Bubbles are then set to False.

Is there a risk that the computation could turn out to be nonsensical as is stated for example in the ElmerModels manual under the keyword section of the Advection-Diffusion equation ?

Best regards
mika
Posts: 230
Joined: 15 Sep 2009, 07:44

Re: Modelpde with no stabilization

Post by mika »

It should be possible to apply bubble augmentation by giving a p-element definition. For example

Element = "p:1 b:1"

creates one elementwise bubble function. This construct doesn't depend on the keyword Bubbles and needs the background mesh consisting of the lowest-order elements.

--Mika
spacedout
Posts: 177
Joined: 30 Mar 2020, 23:27
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Re: Modelpde with no stabilization

Post by spacedout »

Section E.1 of the Elmer Solver manual displays a table giving the number of DOFs as a function of the local polynomial degree p for various elements and for nodes, edges, faces and bubbles. On the other hand,

Element = "n:N'
Element = "e:E'
Element = "f:F'
Element = "b:B'

are allowed under section G.1 which means the number of DOFs is now chosen arbitrarily and is thus independent of p.

I just don't get it. Therefore, I started to read Solin's textbook entitled Higher-order finite element methods. Hopefully all of this will then become clearer.
mika
Posts: 230
Joined: 15 Sep 2009, 07:44

Re: Modelpde with no stabilization

Post by mika »

In Elmer the basic element definition for using the p-version of FEM is just "p:k", where k defines the order of approximation. Elmer then assigns automatically the right numbers of DOFs associated with different geometric entities (edges, faces and element interiors). Mixing the definition "p:k" with "e:E" or "f:F" is not allowed, but exceptionally the number of elementwise bubble functions can be adjusted by the user, so the form "p:k b:B" works. The documentation can be used to check how many bubbles come with a certain polynomial order.

The definitions of types "e:E" or "f:F have been applied to create (vector-valued) finite elements which give either tangential or normal continuity. Then the suitable basis functions are returned by special subroutines (EdgeElementInfo or FaceElementInfo).
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