# Copyright (c) 2005 Johan Hoffman (hoffman@cims.nyu.edu) # Licensed under the GNU GPL Version 2 # # The contiuity equation for the incompressible # Navier-Stokes equations using cG(1)cG(1) # # Compile this form with FFC: ffc NSEContinuity.form. name = "NSEContinuity2D" scalar = FiniteElement("Lagrange", "triangle", 1) vector = FiniteElement("Vector Lagrange", "triangle", 1) constant_scalar = FiniteElement("Discontinuous Lagrange", "triangle", 0) q = BasisFunction(scalar) # test basis function p = BasisFunction(scalar) # trial basis function uc = Function(vector) # linearized velocity f = Function(vector) # force term delta1 = Function(constant_scalar) # stabilization parameter um = mean(uc); # cell mean value of linearized velocity i0 = Index() # index for tensor notation i1 = Index() # index for tensor notation # Bilinear and linear forms a = delta1*dot(grad(q), grad(p))*dx; L = delta1*dot(grad(q), f)*dx - q*uc[i0].dx(i0)*dx - delta1*q.dx(i0)*um[i1]*uc[i0].dx(i1)*dx