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Adaptivity in Numerical Methods for ODEs and PDEs

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UNQ - Uncertainty quantification for complex systems: theory and methodologies

In this talk I will emphasize on the use of adaptive strategies in numerical algorithms to solve systems of ordinary and partial differential equations more efficiently and reliably. After a brief introduction to local and global error control for time integrators general approaches to combine adaptivity in space and time are discussed. Finally, I will speak about recent developments in using adaptive multilevel strategies for PDE -constrained optimization and uncertainty quantification. Throughout my talk I will present numerical results for academic as well as real-life applications including chemical reaction-diffusion systems, regional hyperthermia, electro-cardiology, magneto-quasistatics, glass cooling and complex turbulent flows.



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