From: KIRK, BENJAMIN (JSCEG) (NASA) <benjamin.kirk1@na...>  20051031 17:41:43

Right... For generic quadrature rules we replace \int_\Omega f(x) d\Omega approximately with a sum over {qp} quadrature points. \sum_{qp} f(x_{qp}) w_{qp} J_{qp} where x_{qp} are the locations of the quadrature points in physical space, w_{qp} is the weight of each quadrature point, and J_{qp} is the Jacobian evaluated at the quadrature point (which is not necessarily constant for higherorder mappings from physical to computational space). As John points out, get_JxW returns the product of the weight and the Jacobian for each quadrature point. If you specify a CONSTANT QGauss rule the weight should be 1 and the JxW value should be the Jacobian that you expect. I'd bet you are getting a default 2point rule that has two points, each weighted by 1/2. As for your second question, I'm not sure I understand, but I think you are asking how to use different orders of mapping for the elements vs. the unknowns? (I'm guessing because of the popular entropyproduction you see in 2D subsonic Euler flow over a cylinder when you use a linear map to the reference elements?) In libMesh the elements are mapped with the "natural" Lagrange basis, and the unknowns are what you request. For example, if you solve a problem with CONSTANT MONOMIALS in 2D on Quad9's you will have a solution that is piecewise constant over elements which are mapped quadratically from physical to computational space. Ben Original Message From: libmeshusersadmin@... [mailto:libmeshusersadmin@...] On Behalf Of John Peterson Sent: Monday, October 31, 2005 10:01 AM To: jcch@... Cc: libmeshusers@... Subject: [Libmeshusers] (no subject) jcch@... writes: > Hi, I am trying to implement a RungeKutta Discontinuous Galerkin method > to solve the Euler equations in 1D. > > I try to use the FE classes MONOMIAL and XYZ but I get wrong results for > the jacobian evaluation JxW. > > When we transform > > \int_{x0}^{x1} ... dx = \int_{1}^{+1} ... J dy > > the jacobian is J = dx/dy = ( x1  x0 ) / 2. Hi, you might be looking at the value of JxW? This is the Jacobian multiplied by the Gauss quadrature weighting value. J  This SF.Net email is sponsored by the JBoss Inc. Get Certified Today * Register for a JBoss Training Course Free Certification Exam for All Training Attendees Through End of 2005 Visit http://www.jboss.com/services/certification for more information _______________________________________________ Libmeshusers mailing list Libmeshusers@... https://lists.sourceforge.net/lists/listinfo/libmeshusers 