Hi, Wolfgang,

Thanks a lot. I didn't apply refinement in my code, so there is no hanging 
node problem. As you said, there is a big difference around the boundary. I 
set the boundary value always equal to the initial value which is equal to 
1. The M*old_solution method gives the correct answer which is 1, but the 
second method can not. The attached file is the solution. 

Best,

Xiang

On Tuesday, 7 April 2020 16:03:10 UTC-7, Wolfgang Bangerth wrote:
>
> On 4/7/20 4:58 PM, 孙翔 wrote: 
> > 
> > Do you mean the Dirichlet boundary condition? I applied the boundary 
> condition 
> > after I form the right-hand side vector. I don't think the boundary 
> condition 
> > will lead to different solutions because the right-hand side vector has 
> been 
> > different before I add the boundary conditions. 
>
> "I don't think" is the wrong approach :-) You are seeing something you are 
> not 
> expecting. In other words, what you "expect" is not happening, and so you 
> need 
> to let go of what you think is happening -- you need to *verify* that what 
> you 
> think is happening is happening! That's the whole mind set of debugging 
> problems :-) 
>
> Best 
>   WB 
>
>
> -- 
> ------------------------------------------------------------------------ 
> Wolfgang Bangerth          email:                 bang...@colostate.edu 
> <javascript:> 
>                             www: http://www.math.colostate.edu/~bangerth/ 
>
>

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