Our first approach measures the error in the Poisson equation and drives the mesh-refinement for the coupled system based solely on this error. We use an asymptotically exact residual-based error indicator for elliptic problems which relies on solving local Neumann problems in each element. The solution of the positive-definite linear system for every element is of the size equal to the dimension of the space of 'bubble' functions. The estimator is robust in the sense that it works well for both 1D and 2D problems and in both pre-asymptotic and asymptotic ranges. Also, since the computations are local involving only one or a few neighbouring elements at a time, the implementation is almost completely vectorizable and parallelizable.
Amit Agarwal (agarwal@gloworm.Stanford.EDU)