DOLFIN User Manual - FEniCS Project

Chapter 7Partial differential equations◮ Developer’s note: This chapter is currently being written. . .◮ Developer’s note: Use U for discrete solution and U for correspondingrepresentation in the codeDOLFIN provides a general interface for defining a partial differential equation(PDE) in variational form. The variational form is compiled with FFC,which generates code for the assembly of a matrix and a vector, correspondingto the discretization of the PDE with a user-defined finite element method(FEM), where the basis functions of the FEM space are constructed usingFIAT.7.1 Boundary value problemsAs a prototype of a boundary value problem in R d we consider the scalarPoisson equation with homogeneous Dirichlet boundary conditions− ∆u(x) = f(x) x ∈ Ω ⊂ R d (7.1)u(x) = 0 x ∈ ∂Ω.45