[aspect-devel] Temperature mesh refinement criteria

[Wolfgang Bangerth]

>        Second derivative, I guess you meant second spatial derivative, which 
> would perhaps be the Laplacian in 3D.

Like I said, it's an approximation, so it's neither the full matrix of second 
derivatives nor the Laplacian. But in spirit it's more like the full matrix of 
second derivatives.

> 
>        Then appealing to the energy equation, the Laplacian equates with the 
> material derivative of the Temperature with respect to time..and the 
> mechanical work terms..

Don't look at it in terms of physical quantities. The reasoning for using the 
second derivatives is that when you use finite elements, the approximation 
error is given by

   || u - u_h ||  <=  C h^2  || nabla^2 u ||

where  nabla^2 u  is the matrix of second derivatives of the (exact) solution. 
In other words, the second derivatives are an indicator of the approximation 
error.

Best
  W.

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