Recovery type a posteriori estimates and superconvergence for nonconforming FEM of eigenvalue problems |
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Authors: | Huipo Liu Juan Sun |
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Institution: | 1. Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, Beijing 100088, China;2. College of Mathematics and Computer Science, Hebei University, Baoding 071002, China |
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Abstract: | The main goal of this paper is to present recovery type a posteriori error estimators and superconvergence for the nonconforming finite element eigenvalue approximation of self-adjoint elliptic equations by projection methods. Based on the superconvergence results of nonconforming finite element for the eigenfunction we derive superconvergence and recovery type a posteriori error estimates of the eigenvalue. The results are based on some regularity assumption for the elliptic problem and are applicable to the lowest order nonconforming finite element approximations of self-adjoint elliptic eigenvalue problems with quasi-regular partitions. Therefore, the results of this paper can be employed to provide useful a posteriori error estimators in practical computing under unstructured meshes. |
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Keywords: | Nonconforming finite element Projection methods Eigenvalue A posteriori error estimates Superconvergence |
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