step-11 boundary element

[Alex]

Hi all

I am new to dealii. I have a question on step-11. For a domain with a curved boundary such as step-11 with fe(1), is the boundary element still a bilinear one if mapping order>1? i.e. always 4 dofs on a boundary element? Thanks

Alex

[Wolfgang Bangerth]

You need to distinguish between the element and the mapping. The element's
shape functions are defined on the reference cell, and for a Q1 element
(=fe(1)), there are always 4 shape functions in 2d.

The *mapping* on the other hand is used to describe how shape functions are
transformed from the reference cell to the real cell. This mapping is more
complicated when you have a curved boundary than if you have a straight
boundary, but it does not affect *how many* shape functions there are.

Best
W.

--
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Wolfgang Bangerth email: bang...@colostate.edu
www: http://www.math.colostate.edu/~bangerth/

[Alex]

Thank you. Do you have any recommendation for reference notes or books which explains the math behind mapping? I can see some in Mapping< dim, spacedim > Class Template Reference.

Alex

[Wolfgang Bangerth]

On 7/9/20 8:50 PM, Alex wrote:
> Thank you. Do you have any recommendation for reference notes or books which
> explains the math behind mapping? I can see some in Mapping< dim, spacedim >
> Class Template Reference.

I'm not good with what FE book talks about which, but most FE books will have
sections that cover the idea of "mapping" shape functions. Higher order
mappings are often discussed with keywords such as "isoparametric mappings".