An rp-adaptivity scheme for the finite element analysis of linear elliptic problems
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A finite element analysis methodology employing rp-adaptivity is developed. The p-refinement phase is facilitated through the addition and deletion of general serendipity element edge nodes. The r-refinement phase is based on the reduction of error in the solution using element area as the grid optimization design variable. A series of tiered linked list data structure representations are developed for storing and manipulating the model information. The Zienkiewicz-Zhu error estimator is utilized for determining localized error. A modified superconvergent patch recovery technique is implemented to recover highly accurate nodal gradients utilized in the error estimation phase. Numerical results are presented for an idealized fluid flow problem.
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Maddox, James Roger. "An rp-adaptivity scheme for the finite element analysis of linear elliptic problems." (1995) Master’s Thesis, Rice University. https://hdl.handle.net/1911/17052.