Markus Melenk: A two-scale regularity result for
elliptic problems with periodic microstructure
We present regularity results for the solutions
of a class of elliptic boundary value problems with rapidly
oscillating, periodic coefficients. At the heart
is a detailed analysis of the so-called unit-cell
problem. Applications of our results include mesh design
principles for the generalized FEM (gFEM).
The gFEM introduced by A.-M. Matache and C. Schwab
is a projection method with problem-adapted ansatz space
that can lead to robust convergence, i.e., the convergence is
independent of the coefficients' period. In this talk, we will
review the gFEM and elaborate the bearing of our regularity
results on it.
The work presented is joint with A.-M. Matache.