A posteriori error estimation of the representer method for single-phase Darcy flow

A framework for goal-oriented a posteriori error estimation is developed for the representer method, a data assimilation scheme due to Bennett [A.F. Bennet, Inverse Methods in Physical Oceanography, Cambridge University Press, New York, NY, 1992]. This framework is used to derive an estimate in the case of a mixed finite element approximation of a linear parabolic equation modeling single-phase Darcy flow in porous media. The representer method is computationally expensive, as are most DA schemes; therefore, the error estimates are used to increase computational efficiency by allowing a systematic coarsening of the grids used to calculate the representers. Numerical experiments illustrate the derived estimates and computational savings.