FEniCS Course - FEniCS Project

Deriving a variational problem for Poisson’sequationThe simple recipe is: multiply the PDE by a test function v andintegrate over Ω:∫∫− (∆u)v dx = fv dxΩΩThen integrate by parts and set v = 0 on the Dirichletboundary:∫∫∫∂u− (∆u)v dx = ∇u · ∇v dx −ΩΩ∂Ω ∂n v ds} {{ }=0We find that:∫Ω∫∇u · ∇v dx =Ωfv dx5 / 22