search

0mar / dealiiscale

Finite element simulation of a two-scale problem implemented in deal.II
1 stars 1 forks source link

Obtain convergence estimates for systems without exact solutions #10

Closed 0mar closed 4 years ago

0mar commented 4 years ago

Demonstrating the validity of our multiscale finite element solution requires error estimates. Since we in general don't have any exact solutions for our interesting problems, errors can be estimated by one of two following options.

  1. Compute a very fine solution, pretend this solution is 'exact' and compare L2 difference between this exact solution and coarser solutions

  2. Compute error indicators based on i.e. residuals. This is done (in a different shape) here and can probably be adapted in our case as well.

At this moment I am not sure if 1. gives enough guarantees of convergence, or how to exactly implement 2., but we can experiment.

0mar commented 4 years ago
  1. is implemented in 848bbdc, convergence is as expected. We move forward with this one for now.