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## RE: [Libmesh-users] (no subject)

 RE: [Libmesh-users] (no subject) From: KIRK, BENJAMIN (JSC-EG) (NASA) - 2005-10-31 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 higher-order 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 2-point 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 entropy-production 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: libmesh-users-admin@... [mailto:libmesh-users-admin@...] On Behalf Of John Peterson Sent: Monday, October 31, 2005 10:01 AM To: jcch@... Cc: libmesh-users@... Subject: [Libmesh-users] (no subject) jcch@... writes: > Hi, I am trying to implement a Runge-Kutta 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 _______________________________________________ Libmesh-users mailing list Libmesh-users@... https://lists.sourceforge.net/lists/listinfo/libmesh-users