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

We develop the a posteriori error analysis of stabilised finite element app roximations to linear transport problems via duality arguments. Two alterna tive dual problems are considered: one is based on the formal adjoint of th e hyperbolic differential operator, the other on the transposition of the b ilinear form for the stabilised finite element method. We show both analyti cally and through numerical experiments that the second approach is superio r in the sense that it leads to sharper a posteriori error bounds and more economical adaptively refined meshes. (C) 2000 Elsevier Science S.A. All ri ghts reserved. MSC: 65N12; 65N15; 65N30.