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Content: Multiple scales are ubiquitous in a plurality of processes and phenomena and therefore attract considerable attention both in mathematical and natural science research (see, e.g., http://sfb1114.imp.fu-berlin.de/).

In this lecture we will concentrate on elliptic problems with an highly oscillatory or random behavior due to corresponding coefficient functions. In particular, we will present new results on a class of variational multiscale methods based on subspace decomposition and adaptive multilevel Monte Carlo (MLMC) methods.

If time permits, parabolic problems and stochastic pdes will be also addressed.

Target audience: Students in the Master Course Mathematics or BMS (Phase I)

Prerequisites: Basic knowledge on theory and numerics of elliptic pdes as taught, e.g. in the lecture "Numerik von partiellen Differentialgleichungen (Numerik III)" at FU Berlin

Content: Multiple scales are ubiquitous in a plurality of processes and phenomena and therefore attract considerable attention both in mathematical and natural science research (see, e.g., http://sfb1114.imp.fu-berlin.de/).

In this lecture we will concentrate on elliptic problems with an highly oscillatory or random behavior due to corresponding coefficient functions. In particular, we will present new results on a class of variational multiscale methods based on subspace decomposition and adaptive multilevel Monte Carlo (MLMC) methods.

If time permits, parabolic problems and stochastic pdes will be also addressed.

Target audience: Students in the Master Course Mathematics or BMS (Phase I)

Prerequisites: Basic knowledge on theory and numerics of elliptic pdes as taught, e.g. in the lecture "Numerik von partiellen Differentialgleichungen (Numerik III)" at FU Berlin

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192 284
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