On 2/12/19 12:40 AM, [email protected] wrote:
> 
>  > Constraints are funny and sometimes require deep thought about what exactly
>  > they mean. What happens if you don't apply constraints to the
>  > cell_volume_matrix and cell_gradient_matrix -- i.e., you copy the elements 
> 1:1
>  > into the matrix, without the 'constraints' object? (Like in step-4.)
> I rewrite my code as you say, and the results are:
> |
> Cycle 0:
>     Number of active cells:       20
>     Number of degrees of freedom: 89
>   u square 0: 0.0305621  grad u square 0: 0.256542
> Cycle 1:
>     Number of active cells:       44
>     Number of degrees of freedom: 209
>   u square 1: 0.144303  grad u square 1: 0.49794
> Cycle 2:
>     Number of active cells:       92
>     Number of degrees of freedom: 449
>   u square 2: 0.101366  grad u square 2: 0.477137
> Cycle 3:
>     Number of active cells:       188
>     Number of degrees of freedom: 881
>   u square 3: 0.13305  grad u square 3: 0.529805
> Cycle 4:
>     Number of active cells:       368
>     Number of degrees of freedom: 1737
>   u square 4: 0.145489  grad u square 4: 0.565953
> Cycle 5:
>     Number of active cells:       737
>     Number of degrees of freedom: 3409
>   u square 5: 0.141771  grad u square 5: 0.574863
> Cycle 6:
>     Number of active cells:       1436
>     Number of degrees of freedom: 6705
>   u square 6: 0.171807  grad u square 6: 0.642486
> Cycle 7:
>     Number of active cells:       2729
>     Number of degrees of freedom: 12521
>   u square 7: 0.160819  grad u square 7: 0.625337
> 
> |

Chucui,
you would expect that both the 'u square' and 'grad u square' converge to some 
fixed value, which appears to be the case with the implementation you have here.

Best
  W.

-- 
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Wolfgang Bangerth          email:                 [email protected]
                            www: http://www.math.colostate.edu/~bangerth/

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