Barbara Verfürth

Patrick Henning; Mario Ohlberger; Barbara Verfürth

In this paper, we suggest a new heterogeneous multiscale method (HMM) for the time-harmonic Maxwell equations in locally periodic media. The method is constructed by using a divergence-regularization in one of the cell problems. This allows us to introduce fine-scale correctors that are not subject to a cumbersome divergence-free constraint and which can hence easily be implemented. To analyze the method, we first revisit classical homogenization theory for time-harmonic Maxwell equations and derive a new homogenization result that makes use of the divergence-regularization in the two-scale homogenized equation. We then show that the HMM is equivalent to a discretization of this equation. In particular, writing both problems in a fully coupled two-scale formulation is the crucial starting point for a corresponding numerical analysis of the method. With this approach we are able to prove rigorous a priori error estimates in the

Dietmar Gallistl; Patrick Henning; Barbara Verfürth

\mathbf{H}(\mbox{curl})

Mario Ohlberger; Barbara Verfürth

- and the

Mario Ohlberger; Barbara Verfürth

H^{-1}

Patrick Henning; Mario Ohlberger; Barbara Verfürth

-norm and we derive reliable and efficient localized residual-based a posteriori error estimates.

Mario Ohlberger; Barbara Verfürth

If an elliptic differential operator associated with an

Mario Ohlberger; Barbara Verfürth

{H}({curl})

Patrick Henning; Mario Ohlberger; Barbara Verfürth

-problem involves rough (rapidly varying) coefficients, then solutions to the corresponding

Mario Ohlberger; Ben Schweizer; Maik Urban; Barbara Verfürth

{H}({curl})

Barbara Verfürth

-problem admit typicall...