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A posteriori error estimates for discontinuous Galerkin methods of obstacle problems
Affiliation:1. Department of Mathematics, Pennsylvania State University, University Park, PA 16802, USA;2. School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China;3. Department of Mathematics, University of Iowa, Iowa City, IA 52242, USA;4. School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, Shanxi, 710049, China;5. Department of Mathematics, Rose-Hulman Institute of Technology, Terre Haute, IN 47803, USA;6. Department of Mathematics, Zhejiang University, Hangzhou 310027, China;1. College of Mathematics and Software Science, Sichuan Normal University, Chengdu, Sichuan 610066, China;2. Department of Mathematics, Sichuan University, Chengdu, Sichuan 610021, China;1. Department of Mathematics, National University of Singapore, 10 Lower Kent Ridge Road, Singapore 119076, Republic of Singapore;2. Department of Mathematics, Beijing Institute of Technology, Beijing 100081, People’s Republic of China
Abstract:We present a posteriori error analysis of discontinuous Galerkin methods for solving the obstacle problem, which is a representative elliptic variational inequality of the first kind. We derive reliable error estimators of the residual type. Efficiency of the estimators is theoretically explored and numerically confirmed.
Keywords:Elliptic variational inequality  Discontinuous Galerkin method  A posteriori error estimate  Residual-type error estimator
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