A time- and spaceadaptive algorithm for the linear time-dependent Schrödinger equation (Q1923297)

The linear evolution Schrödinger equation with a time-dependent possibly discontinuous potential on the whole \(n\)-dimensional space is dealt with a finite element based algorithm, which is mesh-adaptive. The mesh control is carried on with the help of a posteriori error estimates. These estimates also show how the computational domain must be enlarged or shrunk as the calculations go on. Some numerical tests carried out for the one-dimensional case are exhibited.