How to Improve Calculation Accuracy

[wang yuan]

Dear all,

I am trying to make a solid finite element solver.

And we all know that the h method and the p method can make the calculation result more accurate, but at the same time consume a lot of computing resources. 

So is there any other method that can effectively improve the accuracy? Do you have any tutorials to share?

Also, if you know of books or articles about nonlinear solvers or fluid-structure interaction methods, can you recommend them to me?

thanks for your replies!

 

[Wolfgang Bangerth]

On 8/7/22 10:36, wang yuan wrote:
> And we all know that the h method and the p method can make the calculation
> result more accurate, but at the same time consume a lot of computing resources.
>
> So is there any other method that can effectively improve the accuracy? Do you
> have any tutorials to share?

There is also r-adaptivity, though it is difficult to implement that in deal.II.

In the end, here are two questions I'd like to suggest you think about:
* I *believe* that what you really care about isn't accuracy, but *accuracy as
a function of something*. You can get any accuracy you want with the finite
element method if you're willing to throw enough computational resources at
it. But usually, there is something that limits you: compute time, memory,
etc. So if you say you want to improve accuracy, my question is first to ask
what your limiting factor is -- in other words, why don't you just use global
refinement?

> Also, if you know of books or articles about nonlinear solvers or
> fluid-structure interaction methods, can you recommend them to me?

I don't have anything specific to offer, but there are several video lectures
on the topic of nonlinear solvers.

Specifically for fluid-structure interaction, people have posted a number of
links on the mailing list before (specifically Thomas Wick) and I would
suggest you search the archives.

Best
WB


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