A Posteriori Error Estimate and hp Adaptivity for Darcy Problems Based on Equilibrated Flux Reconstruction for the H1-Conforming Finite Element Method
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In this work, we apply an a posteriori error estimator based on the Prager Synge theorem for the Darcy problem in the context of hp adaptivity. A simple but innovative strategy is presented for deciding whether to use h or p refinement. The work of Daniel et al. [1] is extended so that the partition of unity can be defined in a mesh with hanging nodes using space restrictions. The proposed method is tested for a wide range of examples: with smooth analytic solution, with steep gradient, with singularity due to a reentrant corner geometry and also with heterogeneous permeability (e.g. material discontinuity). For all the cases, exponential convergence rates are obtained with a very good accuracy for estimating the error.