A posteriori error analysis for stabilised finite element approximations of transport problems

Abstract

We develop the a posteriori error analysis of stabilised finite element approximations to linear transport problems via duality arguments. Two alternative dual problems are considered: one is based on the formal adjoint of the hyperbolic differential operator, the other on the transposition of the bilinear form for the stabilised finite element method. We show both analytically and through numerical experiments that the second approach is superior in the sense that it leads to sharper a posteriori error bounds and more economical adaptively refined meshes.