Optimal local approximation spaces for parabolic problems

Understand

We propose local space-time approximation spaces for parabolic problems that are optimal in the sense of Kolmogorov and may be employed in multiscale and domain decomposition methods.

• The diffusion coefficient can be arbitrarily rough in space and time.
• To construct local approximation spaces we consider a compact transfer operator that acts on the space of local solutions and covers the full time dimension.
• The optimal local spaces are then given by the left singular vectors of the transfer operator.