DOLFIN User Manual - FEniCS Project

DOLFIN User ManualHoffman, Jansson, Logg, Wells12.2 Convection–diffusionThe convection-diffusion equation with Dirichlet and homogeneous Neumannboundary conditions is given by:˙u + b · ∇u − ∇ · (a∇u) = f in Ω × (0, T ],u = g D on Γ 1 × (0, T ],−∂ n u = 0 on Γ 2 × (0, T ],u(·, 0) = u 0 in Ω,(12.3)where the convection is given by the vector b = b(x, t) and the diffusion isgiven by a = a(x, t).The variational formulation is:FIXME:Stabilized convection-diffusionThis is a stabilized FEM-formulation, so the solver can handle convectiondominatedproblems.The time integration is done using cG(1) (Crank-Nicolson).12.2.1 UsageThe API for the convection-diffusion solver:// Create convection-diffusion solverConvectionDiffusionSolver(Mesh& mesh, Function& w, Function& f,BoundaryCondition& bc);// Solve convection-diffusionvoid solve();80