Analisi numerica. -Variational approximation afflux in conforming finite element methods for elliptic partial differential equations: A model problem - Brezzi, F; Hughes, T; Süli, E; Magenes, D (2001)
We consider the approximation of elliptic boundary value problems by conforming finite element methods. A model problem, the Poisson equation with Dirichlet boundary conditions, is used to examine the convergence behavior of flux defined on an internal boundary which splits the domain in two. A variational definition of flux, designed to satisfy local conservation laws, is shown to lead to improved rates of convergence.