Journal
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
Volume 329, Issue -, Pages 195-218Publisher
ELSEVIER SCIENCE SA
DOI: 10.1016/j.cma.2017.10.006
Keywords
Edge elements; Maxwell's equations; Superconvergence; Finite element method
Funding
- Nature Science Foundation of China (NSFC) Key Project [91430213]
- National Science Foundation [DMS-1416742]
- NSFC [11671340, 11626099]
- Hunan Education Department Project [16C0636]
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [1416742] Funding Source: National Science Foundation
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Superconvergence for the second and third order edge elements is investigated on nonuniform rectangular meshes. First, we develop the explicit expression for the Nedelec interpolation based on the hierarchical basis functions. Then we prove that the pointwise interpolation error estimates are one order higher at element Gauss points than the standard analysis can provide. Using the superconvergence at Gauss points, we establish the discrete l(2) norm superconvergence for the solution of Maxwell's equations solved by both the second and third order rectangular edge elements. Numerical results justifying our theoretical analysis are presented. (C) 2017 Elsevier B.V. All rights reserved.
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