NPBS-based adaptive finite element method for static electromagnetic problems

Wang, Fan; Nie, Yufeng; Zhang, Weiwei; Guo, Wenping

doi:10.1080/09205071.2016.1237896

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2019

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“…[14,15,16]. The advantage of BPM is to generate high-quality grids on many complexly bounded 2D and 3D domains and can be easily used in adaptive finite element method and anisotropic problems [17,18,19,20,21]. In addition, due to the natural parallelism of BPM, computational efficiency has been improved greatly to solve large-scale problems [22].…”

Section: Introductionmentioning

confidence: 99%

Provably size-guaranteed mesh generation with superconvergence

Li,

Qi,

Nie

et al. 2019

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The properties and applications of superconvergence on size-guaranteed Delaunay triangulation generated by bubble placement method (BPM), are studied in this paper. First, we derive a mesh condition that the difference between the actual side length and the desired length h is as small as O(h 1+α ) (α > 0). Second, the superconvergence estimations are analyzed on linear and quadratic finite element for elliptic boundary value problem based on the above mesh condition. In particular, the mesh condition is suitable for many known superconvergence estimations of different equations. Numerical tests are provided to verify the theoretical findings and to exhibit the superconvergence property on BPM-based grids.

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