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| In this talk we introduce numerical homogenization methods for a class of nonlinear monotone parabolic multiscale problems with data oscillating rapidly in space. We first introduce a method combining the implicit Euler method in time with a finite element heterogeneous multiscale method in space (coupling macro and micro finite element methods) for which we present optimal fully discrete a priori error estimates in both time and space. The upscaling procedure of the method however relies on nonlinear elliptic cell problems at the microscopic level. As this is computationally costly for practical simulations, we briefly discuss a new linearized scheme that is much more efficient as it only involves linear micro problems. |
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