Seminar in Numerical Analysis: Michael Multerer (USI Lugano)

Numerical aspects of elliptic diffusion problems on random domains

The numerical simulation of physical phenomena is very well understood given that the input data are given exactly. However, in practice, the collection of these data is usually subjected to measurement errors. The goal of uncertainty quantification is to assess those errors and their possible impact on simulation results.In this talk, we address different numerical aspects of uncertainty quantification in elliptic partial differential equations on random domains. Starting from the modelling of random domains via random vector fields, wediscuss how the corresponding Karhunen-Loève expansion can efficiently becomputed. For the discretisation of the partial differential equation, we apply an adaptive Galerkin framework. An a posteriori error estimator is presented, which allows for the problem-dependent iterative refinement of all discretisation parameters and the assessment of the achieved error reduction. The proposed approach is demonstrated in numerical benchmark problems.

For further information about the seminar, please visit this webpage.

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