On Wed, May 15, 2013 at 4:13 PM, John Peterson <[email protected]> wrote:
> On Wed, May 15, 2013 at 11:58 AM, Manav Bhatia <[email protected]> > wrote: > > > > I have attached a pdf which plots the expression for a 2-noded and a > > 3-noded element using Lagrange interpolation functions. The element has > unit > > length. The 2-noded value is constant at 2 for the entire domain of the > > element, while the 3-noded element shows a variation in the element > domain. > > It equals 2 at xi=0, but rises to about 8 on either end. Each quadrature > > point uses the inverse of this function value. > > (I doubt stabilization is actually causing the p-convergence problems > you're seeing, but just to clarify what I was getting at...) > > > You plotted dNi/d(\xi) for these reference elements, where by "\xi" I > mean the reference domain coordinate. > > But to compute the dNi/dx which is actually used in your formula, you > have to multiply dNi/d(\xi) by the inverse jacobian, e.g. > > dNi/dx = dNi/d(\xi) * d(\xi)/dx > > For example: in 1D, a linear Lagrange element has Jacobian dx/d(\xi) = > h/2, inverse d(\xi)/dx = 2/h, and therefore > > dNi/dx = (2/h) * dNi/d(\xi) > > which is O(1/h). > > Hi John, It is dNi/dx that I plotted. Actually, for this 1D case, the dNi/dxi and dNi/dx are simply scaled variants of each other by a constant (the factor 2/h that you mentioned). I do follow your argument for 1/h, but varying polynomial order also varies the tau value (reducing values of tau with higher p). How would that reflect on identifying the h-order-dependence? Or would it stay consistent with h^1 for tau, no matter what p is used? Manav ------------------------------------------------------------------------------ AlienVault Unified Security Management (USM) platform delivers complete security visibility with the essential security capabilities. Easily and efficiently configure, manage, and operate all of your security controls from a single console and one unified framework. Download a free trial. http://p.sf.net/sfu/alienvault_d2d _______________________________________________ Libmesh-users mailing list [email protected] https://lists.sourceforge.net/lists/listinfo/libmesh-users
