BEGIN:VCALENDAR VERSION:2.0 PRODID:-//Sabre//Sabre VObject 4.6.1//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:news1480@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20230418T090618 DTSTART;TZID=Europe/Zurich:20230421T110000 SUMMARY:Seminar in Numerical Analysis: Omar Lakkis (University of Sussex) DESCRIPTION:Least-squares finite element recovery-based methods provide a s imple and practical way to approximate linear elliptic PDEs in nondivergen ce form where standard variational approach either fails or requires techn ically complex modifications.\\r\\nThis idea allows the creation of effici ent solvers for fully nonlinear elliptic equations\, the linearization of which leaves us with an equation in nondivergence form. An important class of fully nonlinear elliptic PDEs can be written in Hamilton--Jacobi--Bell man (Dynamic Programming) form\, i.e.\, as the supremum of a collection of linear operators acting on the unkown.\\r\\nThe least-squares FEM approac h\, a variant of the nonvariational finite element method\, is based on gr adient or Hessian recovery and allows the use of FEMs of arbitrary degree. The price to pay for using higher order FEMs is the loss of discrete-leve l monotonicity (maximum principle)\, which is valid for the PDE and crucia l in proving the convergence of many degree one FEM and finite difference schemes.\\r\\nSuitable functional spaces and penalties in the least-square s's cost functional must be carefully crafted in order to ensure stability and convergence of the scheme with a good approximation of the gradient ( or Hessian) under the Cordes condition on the family of linear operators b eing optimized.\\r\\nFurthermore\, the nonlinear operator which is not nec essarily everywhere differentiable\, must be linearized in appropriate fun ctional spaces using semismooth Newton or Howard's policy iteration method . A crucial contribution of our work\, is the proof of convergence of the semismooth Newton method at the continuum level\, i.e.\, on infinite dimes ional functionals spaces. This allows an easy use of our non-monotone sche mes which provides convergence rates as well as a posteriori error estimat es.\\r\\n\\r\\nFor further information about the seminar\, please visit th is webpage [t3://page?uid=1115]. X-ALT-DESC:

Least-squares finite element recovery-based methods provide a simple and practical way to approximate linear elliptic PDEs in nondiverg ence form where standard variational approach either fails or requires tec hnically complex modifications.

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This idea allows the creation of e fficient solvers for fully nonlinear elliptic equations\, the linearizatio n of which leaves us with an equation in nondivergence form. An important class of fully nonlinear elliptic PDEs can be written in Hamilton--Jacobi- -Bellman (Dynamic Programming) form\, i.e.\, as the supremum of a collecti on of linear operators acting on the unkown.

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The least-squares FEM approach\, a variant of the nonvariational finite element method\, is bas ed on gradient or Hessian recovery and allows the use of FEMs of arbitrary degree. The price to pay for using higher order FEMs is the loss of discr ete-level monotonicity (maximum principle)\, which is valid for the PDE an d crucial in proving the convergence of many degree one FEM and finite dif ference schemes.

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Suitable functional spaces and penalties in the l east-squares's cost functional must be carefully crafted in order to ensur e stability and convergence of the scheme with a good approximation of the gradient (or Hessian) under the Cordes condition on the family of linear operators being optimized.

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Furthermore\, the nonlinear operator wh ich is not necessarily everywhere differentiable\, must be linearized in a ppropriate functional spaces using semismooth Newton or Howard's policy it eration method. A crucial contribution of our work\, is the proof of conve rgence of the semismooth Newton method at the continuum level\, i.e.\, on infinite dimesional functionals spaces. This allows an easy use of our non -monotone schemes which provides convergence rates as well as a posteriori error estimates.

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For further information about the seminar\, pl ease visit this webpage.

DTEND;TZID=Europe/Zurich:20230421T120000 END:VEVENT END:VCALENDAR