DOLFIN User Manual - FEniCS Project

DOLFIN User ManualHoffman, Jansson, Logg, WellsFIXME:List solvers, then present in detail, include lots of nice images withsolver output12.1 Poisson’s equationPoisson’s equation with Dirichlet and homogeneous Neumann boundary conditions:The variational formulation is given by−∆u = f in Ω,u = g D on Γ 1 ,(12.1)−∂ n u = 0 on Γ 2∫∇u · ∇v dx = ∫ fv dx ∀v. (12.2)Ω ΩThe boundary conditions are enforced strongly and thus don’t appear in thevariational formulation.12.1.1 UsageThe API for the Poisson solver:// Create Poisson solverPoissonSolver(Mesh& mesh, Function& f, BoundaryCondition& bc);// Solve Poisson’s equationvoid solve();// Solve Poisson’s equation (static version)static void solve(Mesh& mesh, Function& f, BoundaryCondition& bc);78