Abstract
In this contribution, we formulate a heterogeneous multiscale finite element method (HMM) for monotone elliptic operators. This is done in the general concept of HMM, which was initially introduced by E and Engquist [E, Engquist, The heterogeneous multiscale methods, Commun. Math. Sci., 1(1):87–132, 2003]. Since the straightforward formulation is not suitable for a direct implementation in the nonlinear setting, we present a corresponding algorithm, which involves the computation of additional cell problems. The algorithm is validated by numerical experiments and can be used to effectively determine homogenized solutions.
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