Mon, October 15, 2018
Public Access

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2:00pm [2:30pm] Prof. Jerome Droniou
Description:
Speaker: Prof. Jerome Droniou Affiliation: Monash University, Melbourne Time: Monday (15-10-18), 2.30 PM-3.30 PM. Venue: Ramanujan Hall. Tiitle: What the second Strang lemma and the Aubin-Nitsche trick should be Abstract: The second Strang lemma gives an error estimate for linear problems written in variational formulation, such as elliptic equations. It covers both conforming and non-conforming methods, it is widely spread in the finite element community, and usually considered as the starting point of any convergence analysis. For all its potency, it has a number of limitations which prevents its direct application to other popular methods, such as dG methods, Virtual Element Methods, Hybrid High Order schemes, Mimetic Methods, etc. Ad-hoc adaptations can be found for some of these methods, but no general `second Strang lemma' has been developed so far in a framework that covers all these schemes, and others, at once. In this talk, I will present a `third Strang lemma' that is applicable to any discretisation of linear variational problems. The main idea to develop a framework that goes beyond FEM and covers schemes written in a fully discrete form is to estimate, in a discrete energy norm, the difference between the solution to the scheme and some interpolant of the continuous solution. I will show that this third Strang lemma is much simpler to prove, and use, than the second Strang lemma. It also enables us to define a clear notion of consistency, including for schemes for which such a notion was not clearly defined so far, and for which the Lax principle `stability + consistency implies convergences' holds. I will also extend the analysis to the Aubin-Nitsche trick, presenting a generalisation of this trick that covers fully discrete schemes and provides improved error estimates in a weaker norm than the discrete energy norm. We will see that the terms to estimate when applying this Aubin-Nitsche trick are extremely similar to those appearing when applying the third Strang lemma; work done in the latter case can therefore be re-invested when looking for improved estimates in a weaker norm. I will conclude by briefly presenting applications of the third Strang lemma and the abstract Aubin-Nitsche trick to discontinuous Galerkin and Finite Volume methods.

3:00pm
4:00pm [4:00pm] Prof. Palash Ghosh Centre for Quantitative Medicine DUKE-NUS Medical School National University of Singapore
Description:
Statistics Seminar. Speaker: Prof. Palash Ghosh Centre for Quantitative Medicine DUKE-NUS Medical School National University of Singapore Date: Monday, 15/10/18. Time: 4:00--5:00 pm. Venue: Ramanujan Hall Title: Dynamic Generalized Odds-Ratio (dGOR): A novel approach to assess Dynamic Treatment Regimes (DTR) with An Ordinal Outcome. Abstract: See Attachment.

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