Aspects of the Localized Orthogonal Decomposition

Multiscale problems arise in many applications and means that a partial differential equation contains a coefficient that varies on a small scale. Standard numerical methods have to resolve this scale to yield reasonable results. The localized orthogonal decomposition (LOD) employs problem-dependent pre-computed test functions that allow for a reasonable approximation of the solution on a coarse mesh. The method allows for a rigorous error an alysis.

This talk introduces the LOD and discusses some possible generalizations.