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:news1703@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20241001T122056 DTSTART;TZID=Europe/Zurich:20241025T110000 SUMMARY:Seminar in Numerical Analysis: Andreas Veeser (University of Milan) DESCRIPTION:In the context of finite element methods for boundary value pro blems\, the goal of an a posteriori error analysis is to derive a so-calle d error estimator. Such an estimator should be a quantity that is computab le in terms of the problem data and the finite element solution and equiva lent to its error. Almost all error estimators available in literature\, h owever\, do not meet these requirements. Indeed\, equivalence is typically verified only up to so-called (data) oscillations and their presence has been viewed as the price of computability.\\r\\nThe talk will consist of t wo parts. The first part will argue that the infinite-dimensional nature o f the problem data is an obstruction to computability\, while the typical form of oscillations obstructs equivalence. In other words: the desirable but missing unspoiled equivalence is not only a technical problem but does not hold for the involved oscillations.\\r\\nThe second part will then pr esent the new approach to a posteriori error estimation proposed by [1]. I ts resulting estimators are equivalent to the error and consist of two par ts\, where the first one is of finite-dimensional nature and thus computab le\, while the second one is a new form of data oscillation\, which is alw ays smaller that the old one and whose computability hinges on the knowled ge of the problem data. This splitting of the error estimator is also conv enient in guiding adaptive algorithms\; cf. [2].\\r\\n[1] C. Kreuzer\, A. Veeser\, Oscillation in a posteriori error estimation\, Numer. Math. 148 ( 2021)\, 43-78 [2] A. Bonito\, C. Canuto\, R. H. Nochetto\, A. Veeser\, Ada ptive finite element methods\, Acta Numerica 33 (2024)\, 163-485.\\r\\n\\r \\nFor further information about the seminar\, please visit this webpage [ t3://page?uid=1115]. X-ALT-DESC:

In the context of finite element methods for boundary value p roblems\, the goal of an a posteriori error analysis is to derive a so-cal led error estimator. Such an estimator should be a quantity that is comput able in terms of the problem data and the finite element solution and equi valent to its error. Almost all error estimators available in literature\, however\, do not meet these requirements. Indeed\, equivalence is typical ly verified only up to so-called (data) oscillations and their presence ha s been viewed as the price of computability.

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The talk will consist of two parts. The first part will argue that the infinite-dimensional nat ure of the problem data is an obstruction to computability\, while the typ ical form of oscillations obstructs equivalence. In other words: the desir able but missing unspoiled equivalence is not only a technical problem but does not hold for the involved oscillations.

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The second part will then present the new approach to a posteriori error estimation proposed b y [1]. Its resulting estimators are equivalent to the error and consist of two parts\, where the first one is of finite-dimensional nature and thus computable\, while the second one is a new form of data oscillation\, whic h is always smaller that the old one and whose computability hinges on the knowledge of the problem data. This splitting of the error estimator is a lso convenient in guiding adaptive algorithms\; cf. [2].

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[1] C. Kr euzer\, A. Veeser\, Oscillation in a posteriori error estimation\, Numer. Math. 148 (2021)\, 43-78
[2] A. Bonito\, C. Canuto\, R. H. Nochetto\ , A. Veeser\, Adaptive finite element methods\, Acta Numerica 33 (2024)\, 163-485.

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For further information about the seminar\, please visi t this webpage.

DTEND;TZID=Europe/Zurich:20241025T120000 END:VEVENT END:VCALENDAR