Implicit interpolation error-based error estimation for reaction-diffusion equations in two space dimensions Original Research Article

Several authors have proposed an error estimation strategy for the finite element method applied to linear reaction-diffusion equations in two space dimensions based on an odd/even-order dichotomy principle. For odd-order approximations the estimates are computed directly. For even-order approximations a second solution is computed. Although both estimators are asymptotically exact the latter are more robust than the former. Herein the even-order method is extended to all orders greater than one, thereby recovering robustness for odd orders. Proofs of asymptotic exactness are extended to nonlinear reaction-diffusion equations. Computational results demonstrating their effectiveness are presented.