error estimate

[Christophe Geuzaine]

Lin Ji wrote:
> 
> Hi, Christophe,
>     To follow up a previous discussion on error estimate, can we ask GetDP to
> provide the error estimation or the number of valid digits of the solution?
>     As I understand, to increase the accuracy of solution, we can either
> refine the mesh or raise the local interpolation order. So, how do we define
> a higher interpolation order in GetDP? What is the default order for solving
> the wave equation example you sent us?  Thanks.

Error estimation in finite element methods is not as simple as 'knowing
the number of valid digits of the solution'. You should ask
Jean-Francois to give you a small presentation on the topic (it was
--partially-- the subject of his PhD).

In the example I sent you, the interpolation order is 1. To increase the
interpolation order, you need to complete the function space definition
with higher order basis functions. Here is for example the function
space for a 2nd order interpolation:

FunctionSpace {
  { Name Hgrad; Type Form0;
    BasisFunction {
      { Name sn; NameOfCoef un; Function BF_Node; 
        Support Region[{Omega,Gamma_f}]; Entity NodesOf[All]; }
      { Name sn2; NameOfCoef un2; Function BF_Node_2E; 
        Support Region[{Omega,Gamma_f}]; Entity EdgesOf[All]; }
    }
    Constraint {
      { NameOfCoef un; EntityType NodesOf ; NameOfConstraint u; }
      { NameOfCoef un2; EntityType EdgesOf ; NameOfConstraint u2; }
    }
  }
}

and you should not forget to impose the constraints on the additional
degrees of freedom (i.e. with the constraint 'u2').

My best,

Christophe


-- 
Christophe Geuzaine

Tel: 32 (0) 4 366 37 10    http://geuz.org
Fax: 32 (0) 4 366 29 10    mailto:Christophe.Geuzaine at ulg.ac.be