I'm going to ask some beginners' questions.
Adaptive mesh can save many DOFs than a uniform mesh. But it also needs to solve linear systems changing with mesh adaptive process. Is this not problem?
Now suppose we are going to solve the problem a lot of times with different multiple source/boundary/initial data. What techniques are useful for adaptive mesh to further reduce costs?
I once heard a lecture given by Hackbusch who proposed to just use a very fine uniform mesh and make use of some low rank property of the matrix to compute its inverse. The number of DOFs sounds crazy but the method seems to work well.
Would someone shares his/her experiences?