A Localised Orthogonal Decomposition Method for Heterogeneous Mixed-Dimensional Problems

Abstract: In this talk, we present a model for solving mixed-dimensional elliptic problems with highly heterogeneous coefficients, a type of problem that commonly appears in e.g. modelling of fractured porous media but can be computationally challenging to solve numerically. Thin structures are modelled as lower-dimensional interfaces embedded in a higher-dimensional bulk domain, leading to the mixed-dimensional model problem.

Our method is based on the Localised Orthogonal Decomposition (LOD) method and constructs locally supported basis functions on a coarse mesh that does not resolve the fine-scale variations of the coefficients. The basis functions are adapted to the problem at hand and thus carries the fine-scale information in order to ensure optimal convergence with respect to the coarse mesh. This method leads to an exponentially decaying localisation error. We present numerical experiments to validate the theoretical findings.

numerical analysisoptimization and control

Audience: researchers in the topic

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CAM seminar

Series comments: Online streaming via zoom on exceptional cases if requested. Please contact the organizers at the latest Monday 11:45.

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