BEGIN:VCALENDAR VERSION:2.0 PRODID:-//Sabre//Sabre VObject 4.5.8//EN CALSCALE:GREGORIAN BEGIN:VTIMEZONE TZID:Europe/Zurich X-LIC-LOCATION:Europe/Zurich TZURL:http://tzurl.org/zoneinfo/Europe/Zurich BEGIN:DAYLIGHT TZOFFSETFROM:+0100 TZOFFSETTO:+0200 TZNAME:CEST DTSTART:19810329T020000 RRULE:FREQ=YEARLY;BYMONTH=3;BYDAY=-1SU END:DAYLIGHT BEGIN:STANDARD TZOFFSETFROM:+0200 TZOFFSETTO:+0100 TZNAME:CET DTSTART:19961027T030000 RRULE:FREQ=YEARLY;BYMONTH=10;BYDAY=-1SU END:STANDARD END:VTIMEZONE BEGIN:VEVENT UID:news1570@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20231127T102321 DTSTART;TZID=Europe/Zurich:20231208T110000 SUMMARY:Seminar in Numerical Analysis: Martin Vohralik (Inria Paris) DESCRIPTION:A posteriori estimates enable to certify the error committed in a numerical simulation. In particular\, the equilibrated flux reconstruct ion technique yields a guaranteed error upper bound\, where the flux\, obt ained by a local postprocessing\, is of independent interest since it is a lways locally conservative. In this talk\, we tailor this methodology to m odel nonlinear and time-dependent problems to obtain estimates that are ro bust\, i.e.\, of quality independent of the strength of the nonlinearities and the final time. These estimates include\, and build on\, common itera tive linearization schemes such as Zarantonello\, Picard\, Newton\, or M- and L-ones. We first consider steady problems and conceive two settings: w e either augment the energy difference by the discretization error of the current linearization step\, or we design iteration-dependent norms that f eature weights given by the current iterate. We then turn to unsteady prob lems. 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 addresse d here. Numerical experiments illustrate the theoretical findings all alon g the presentation. Details can be found in [1-4].\\r\\nA. Ern\, I. Smears \, M. Vohralík\, Guaranteed\, locally space-time efficient\, and polynomi al-degree robust a posteriori error estimates for high-order discretizatio ns of parabolic problems\, SIAM J. Numer. Anal. 55 (2017)\, 2811–2834.\\ r\\nA. Harnist\, K. Mitra\, A. Rappaport\, M. Vohralík\, Robust energy a posteriori estimates for nonlinear elliptic problems\, HAL Preprint 04033 438\, 2023.\\r\\nK. Mitra\, M. Vohralík\, A posteriori error estimates fo r the Richards equation\, Math. Comp. (2024)\, accepted for publication.\\ r\\nK. Mitra\, M. Vohralík\, Guaranteed\, locally efficient\, and robust a posteriori estimates for nonlinear elliptic problems in iteration-depend ent norms. An orthogonal decomposition result based on iterative lineariza tion\, HAL Preprint 04156711\, 2023.\\r\\n\\r\\nFor further information a bout the seminar\, please visit this webpage [t3://page?uid=1115]. X-ALT-DESC:

A posteriori estimates enable to certify the error committed in a numerical simulation. In particular\, the equilibrated flux reconstru ction technique yields a guaranteed error upper bound\, where the flux\, o btained 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 nonlineariti es and the final time. These estimates include\, and build on\, common ite rative 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 th e current linearization step\, or we design iteration-dependent norms that feature weights given by the current iterate. We then turn to unsteady pr oblems. Here we first consider the linear heat equation and finally move t o the Richards one\, that is doubly nonlinear and exhibits both parabolic –hyperbolic and parabolic–elliptic degeneracies. Robustness with respe ct to the final time and local efficiency in both time and space are addre ssed here. Numerical experiments illustrate the theoretical findings all a long the presentation. Details can be found in [1-4].

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A. Ern\, I. Smears\, M. Vohralík\, Guaranteed\, locally space-time efficient\, and po lynomial-degree robust a posteriori error estimates for high-order discret izations of parabolic problems\, SIAM J. Numer. Anal. 55< /strong> (2017)\, 2811–2834.

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A. Harnist\, K. Mitra\, A. Rappapor t\, M. Vohralík\, Robust energy a posteriori estimates for nonlinear elli ptic problems\, HAL Preprint \;04033438\, 2023.

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K. Mitra\, M. Vohralík\, A posteriori error estimates for the Richards equation\, M ath. Comp. (2024)\, accepted for publication.

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K. Mitra\, M. V ohralík\, Guaranteed\, locally efficient\, and robust a posteriori estima tes for nonlinear elliptic problems in iteration-dependent norms. An ortho gonal decomposition result based on iterative linearization\, HAL Preprint  \;04156711\, 2023.

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For further information about the semina r\, please visit this webpage.

DTEND;TZID=Europe/Zurich:20231208T120000 END:VEVENT END:VCALENDAR