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Numerical Analysis and PDE

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All talks will be on Thursdays at 10:00am in Ewing Hall, Room 336.​

Want to suggest a speaker? Send email to one of the organizers:  Fran​cisco-Javier Sayas or Jingmei Qiu

Information about the Courtyard Newark - University of Delaware Hotel


 

 

Joshua Padgett, Texas Tech UniversityJoshua Padgett, Texas Tech UniversityEWG 336Title: Operator splitting methods for approximating singular nonlinear differential equations <br><br> Abstract: Operator splitting techniques were originally introduced in an effort to save computational costs in numerical simulations. Classically, such methods were restricted to dimensional splitting of evolution operators. However, these methods have since been extended to allow for splitting of problems involving nonlinear operators which evolve on vastly different time scales. In this talk I will introduce the notion of nonlinear operator splitting and rigorously justify the approach by considering some techniques from Lie group theory. This is a nonstandard presentation that should also be accessible to graduate students. The second half of the talk will provide results concerning two very interesting applications of operator splitting techniques: nonlinear stochastic problems and singular combustion problems. The former problems have traditionally been plagued with low-order techniques with restrictive regularity conditions, while the latter have the need for strongly adaptive methods which recover important qualitative properties. We will discuss in detail how operator splitting provides solutions to these issues, while also being straightforward to implement.11/29/2018 3:00:00 PM11/29/2018 4:00:00 PMFalse
Norbert Heuer, Pontificia Universidad Catolica de ChileNorbert Heuer, Pontificia Universidad Catolica de ChileEWG336<br><br>Title:A DPG method for the Kirchhoff-Love plate bending problem<br><br> Abstract:Recently we have developed and analyzed an ultraweak variational formulation for a variant of the Kirchhoff–Love plate bending model. Based on this formulation, we introduced a discretization of the discontinuous Petrov–Galerkin type with optimal test functions (DPG), and proved the well-posedness of the ultraweak formulation and quasi-optimal convergence of the DPG scheme. Essential for the analysis is the appropriate treatment of inherent traces, jumps and trace spaces. A major difficulty stems from the fact that the bending tensor variable has a twice-iterated divergence in L2 but that its (single) divergence is less regular in general. <br><br> We will give a brief introduction to the DPG method, along with its advantages and challenges. We then discuss the plate bending problem and the ideas that led to our variational formulation and corresponding discretization. Some numerical experiments will illustrate convergence properties. This talk is based on a joint work with Thomas Führer (Pontificia Universidad Católica de Chile) and Antti Niemi (University of Oulu, Finland. )12/13/2018 3:00:00 PM12/13/2018 4:00:00 PMFalse

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