Hi Guys I believe chapter 3 talks about the design of the bases and chapter 3 talks about the integration and differentiation techniques. I attach a pre-draft of both chapters for your reference. Cheers, Spencer. Spencer Sherwin FREng, FRAeS Head of Aerodynamics Section, Director of Research Computing Service, Professor of Computational Fluid Mechanics, Department of Aeronautics, South Kensington Campus, Imperial College London, SW7 2AZ, UK Phone: +44 (0)20 7594 5052 http://www.imperial.ac.uk/people/s.sherwin/ On 19 Jul 2020, at 23:00, Yong Wang <yongwang.ttu@gmail.com<mailto:yongwang.ttu@gmail.com>> wrote: Dear Ashock, I presume that the triangular elements also use the Lobatto type quadrature points like rectangular elements and had the question. Thanks a lot for your clarification and references. Best wishes, Yong Wang On Sun, Jul 19, 2020 at 1:34 PM ashok jallepalli <ash.nani@gmail.com<mailto:ash.nani@gmail.com>> wrote: Hi Yong, Below is the reference on how quadrature points are selected in Nektar++ for a 2D element. The number of quadrature points in your case is given by 5x6 = 30 points. A short explanation: (1) Nektar uses collapsed coordinates. - The quadrature points are first mapped on a quad and then collapsed to a triangle. - Gauss Radui points are chosen such that that there is no quadrature point at the collapsed vertex. (2) 3 chapter (could be 4th) in this book is an interesting read about how quadrature points are selected while exactly representing the maximum polynomial appropriately. Book chapter (Reference explains in detail) Spectral/hp Element Methods for Computational Fluid Dynamics: Second Edition (Numerical Mathematics and Scientific Computation) Nektar++ paper (Below reference also explains, but not as complete as the book chapter) https://reader.elsevier.com/reader/sd/pii/S0010465515000533?token=2E0FEFC370... Cheers, Ashok. On Sun, Jul 19, 2020 at 9:44 AM Yong Wang <yongwang.ttu@gmail.com<mailto:yongwang.ttu@gmail.com>> wrote: This email from yongwang.ttu@gmail.com<mailto:yongwang.ttu@gmail.com> originates from outside Imperial. Do not click on links and attachments unless you recognise the sender. If you trust the sender, add them to your safe senders list<https://spam.ic.ac.uk/SpamConsole/Senders.aspx> to disable email stamping for this address. Hello, I am processing the chk file (.fld file) produced by Nektar++ for postprocessing and the mesh I used is a collection of 2D triangular elements with a number of modes of 6 (max. polynomial order = 5). I have a question about the total number of quadrature points in the triangular element: results from the chk file show that each element has totally 30 quadrature points (instead of 31), and coordinates of these points are plotted in the following figure. It seems that these quadrature points don't include the singular point. I wonder why is this the case and could someone kindly recommend references about this issue? It will help me a lot to understand the results generated by Nektar++. Thanks a lot. Best wishes, Yong Wang <image.png> _______________________________________________ Nektar-users mailing list Nektar-users@imperial.ac.uk<mailto:Nektar-users@imperial.ac.uk> https://mailman.ic.ac.uk/mailman/listinfo/nektar-users _______________________________________________ Nektar-users mailing list Nektar-users@imperial.ac.uk<mailto:Nektar-users@imperial.ac.uk> https://mailman.ic.ac.uk/mailman/listinfo/nektar-users