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January 25 Math Colloquium

Mukesh Kumar, CofC

Superconvergence, Post-processing, and A Posteriori Error Estimators in Isogeometric Analysis

In this talk, we first address the existence of superconvergent points in the computed finite element solution based on B-splines and LR B-splines for elliptic model problems. Then, we present some post-processing procedures for improving the derivatives (or gradient) of the isogeometric finite element solution where the Superconvergent Patch Recovery (SPR) procedure will be the main focus. In particular, we show that our SPR procedure for the improvement of derivatives fulfills the desired consistency criteria set by Ainsworth and Craig, Numerische Mathematik, 1992. At the end, we develop a posteriori error estimator where the improved gradient obtained from the proposed recovery procedures is used. Numerical results are presented to illustrate the efficiency of using SPR procedure for the improvement of derivatives (or gradient) of computed solution in isogeometric analysis. Then the proposed a posteriori error estimator based adaptive refinement methodology is tested to solve some regular and singular elliptic benchmark problems.
Joint work with Trond Kvamsdal and Kjetil Andre Johannessen

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