On the Implementation of a Heterogeneous Multi-scale Finite Element Method for Nonlinear Elliptic Problems [chapter]

Patrick Henning, Mario Ohlberger
2012 Advances in DUNE  
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): 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
more » ... blems. The algorithm is validated by numerical experiments and can be used to effectively determine homogenized solutions.
doi:10.1007/978-3-642-28589-9_11 fatcat:pdx7uocnyfa7ra3qr6tpz2af5u