Hp-adaptive finite element methods require error estimates of the solution at the current order and one order higher. Hierarchical-based estimation strategies have proved effective in computing errors at the current order for nonlinear parabolic equations. Recently a new approach, interpolation error-based (IEB) error estimation, for constructing a posteriori error estimates at both orders has been developed for linear reaction-diffusion equations. The main results are: (i) IEB error estimation can be applied to nonlinear reaction-diffusion equations in one space dimension; (ii) the hierarchical estimator is an implicit IEB method and thus, works for reaction-diffusion problems; (iii) a hierarchical extension for computing higher–order error estimates is asymptotically exact. Computational results illustrating the theory and comparing the implicit (hierarchical) strategy with the earlier explicit IEB methods are presented.
Copyright 2004, Walter de Gruyter
