The support for time-dependent problems is still rudimentary.
Especially, it is not yet incorporated in the solution strategy using
solve. For setting up a Rothe method by hand, you may use code
like the following which solves a one-dimensional heat equation with
zero right-hand side and some initial values:
(let* ((dim 1) (levels 4) (order 2) (problem (cdr-model-problem dim :initial #'(lambda (x) #I(sin(2*pi*x^^2))) :reaction 0.0 :source #m(0.0))) (rothe (make-instance '<rothe> :model-time 0.0 :time-step 0.01 :stationary-success-if `(> :nr-levels ,levels) :success-if '(>= :step 20) :output t :plot t))) (storing (iterate rothe (blackboard :problem problem :fe-class (lagrange-fe order) :plot-mesh nil :output t))))
First, the mesh is built up to approximate the initial values until given criteria are met (here the number of levels is prescribed). Then a time-stepping scheme with the implicit Euler method and uniform time-steps is used to approximate the solution in time.