Local boundary value problems for the error in FE approximation of non-linear diffusion systems

In this work we investigate the a posteriori error estimation for a class of non-linear, multicomponent diffusion operators, which includes the Stefan–Maxwell equations. The local error indicators for the global error are based on local boundary value problems, which are chosen to approximate either the global residual of the finite element approximation or the global linearized error equation. Using representative numerical examples, it is shown that the error indicators based on the latter approach are more accurate for estimating the global error for this problem class as the problem becomes more non-linear, and can even produce better adaptive mesh refinement (AMR). In addition, we propose a new local error indicator for the error in output functionals that is accurate, inexpensive to compute, and is suitable for AMR, as demonstrated by numerical examples. Copyright q 2007 John Wiley & Sons, Ltd