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Abstract
Following the description of a-posteriori error estimates in [1] , this article describes an automatic adaptive h-type mesh refinement and coarsening procedure with directional sensitivity, based on the estimated error and solution gradients. Mesh adaptation operates on hexahedra and degenerate hexahedra by hierarchically splitting cells into two, four, or eight new cells and uses "1-irregularity" to preserve mesh smoothness. Arbitrary coarsening is based on cell pairing and controlled by the estimated error distribution and geometric considerations. The method is tested on two test cases in 2-D to examine its error reduction rate and the quality of refined meshes.