Abstract:
A posteriori estimates enable to certify the error committed in a numerical simulation. In particular, the equilibrated flux reconstruction technique yields a guaranteed error upper bound, where the flux, obtained by a local postprocessing, is of independent interest since it is always locally conservative. In this talk, we tailor this methodology to model nonlinear and time-dependent problems to obtain estimates that are robust, i.e., of quality independent of the strength of the nonlinearities and the final time. These estimates include, and build on, common iterative linearization schemes such as Zarantonello, Picard, Newton, or M- and L-ones. We first consider steady problems and conceive two settings: we either augment the energy difference by the discretization error of the current linearization step, or we design iteration-dependent norms that feature weights given by the current iterate. We then turn to unsteady problems. Here we first consider the linear heat equation and finally move to the Richards one, that is doubly nonlinear and exhibits both parabolic-hyperbolic and parabolic-elliptic degeneracies. Robustness with respect to the final time and local efficiency in both time and space are addressed here. Numerical experiments illustrate the theoretical findings all along the presentation. Details can be found in [1-4].A. Ern, I. Smears, M. Vohralík, Guaranteed, locally space-time efficient, and polynomial-degree robust a posteriori error estimates for high-order discretizations of parabolic problems, SIAM J. Numer. Anal.55 (2017), 2811-2834.A. Harnist, K. Mitra, A. Rappaport, M. Vohralík, Robust energy a posteriori estimates for nonlinear elliptic problems, HAL Preprint 04033438, 2023.K. Mitra, M. Vohralík, A posteriori error estimates for the Richards equation, Math. Comp. (2024), accepted for publication.K. Mitra, M. Vohralík, Guaranteed, locally efficient, and robust a posteriori estimates for nonlinear elliptic problems in iteration-dependent norms. An orthogonal decomposition result based on iterative linearization, HAL Preprint 04156711, 2023. For further information about the seminar, please visit this webpage.

11:00 • Universität Basel

ETH Zürich

External FLAIR Seminar

Fabian Pedregosa

The Mysterious Optimization Dynamics of Deep Learning abstract

13:15 • EPF Lausanne GA 3 21

Université de Genève

Physical Mathematics Seminar

Georgios Moschidis (EPFL)

Turbulence in general relativity abstract

14:00 • Université de Genève, Conseil Général 7-9, Room 1-07

ETH Zürich

Number Theory Seminar

Dr. Paul Kiefer (Bielefeld University)

Injectivity of the Kudla-Millson-Lift in genus two abstract

14:15 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 43

EPF Lausanne

Seminar of Analysis

Denis Serre (ENS Lyon)

Dispersion and regularity for scalar conservation laws in several space dimensions abstract

14:15 • EPF Lausanne, MA B1 11

Université de Genève

Séminaire "Fables Géométriques"

Francesca Carocci (UNIGE)

Degenerations of Limit linear series Résumé abstract

14:30 • Université de Genève, salle 06-13

EPF Lausanne

Statistics Seminar

Eardi Lila (University of Washington)

A functional data approach to identifying Alzheimer\'s disease from multimodal cortical surface data abstract

15:15 • EPF Lausanne, MA A3 30

ETH Zürich

Algebraic Geometry and Moduli Seminar

Yannick Schuler (University of Sheffield)

Gromov-Witten theory and the refined topological string abstract

16:00 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 43

address: Alessandra Naldi Windler, Departement Mathematik, HG G 51.4, ETH Zurich, Raemistrasse 101, CH-8092 Zurich
email: bulletin@math.ch | phone: +41 44 632 3684 | url: https://math.ch

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