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Volume 17, Issue 2
Provably Size-Guaranteed Mesh Generation with Superconvergence

Xiangrong Li, Nan Qi, Weiwei Zhang & Yufeng Nie

Int. J. Numer. Anal. Mod., 17 (2020), pp. 236-253.

Published online: 2020-02

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  • Abstract

The mesh conditions of high-quality grids generated by bubble placement method (BPM) and their superconvergence properties are studied in this paper. A mesh condition that for each pair of adjacent triangles, the lengths of any two opposite edges differ only by a high order of the parameter $h$ is derived. Furthermore, superconvergence estimations are analyzed on both linear and quadratic finite elements for elliptic boundary value problems under the above mesh condition. In particular, the mesh condition is found to be applicable to many known superconvergence estimations under different types of equations. Finally, numerical examples are presented to demonstrate the superconvergence properties on BPM-based grids.

  • Keywords

Bubble placement method, mesh condition, superconvergence estimation.

  • AMS Subject Headings

65N50, 65N60, 65N15

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

xiangrong@mail.nwpu.edu.cn (Xiangrong Li)

Nan.Qi@sdu.edu.cn (Nan Qi)

wwzhang@nwpu.edu.cn (Weiwei Zhang)

yfnie@nwpu.edu.cn (Yufeng Nie)

  • BibTex
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  • TXT
@Article{IJNAM-17-236, author = {Li , XiangrongQi , NanZhang , Weiwei and Nie , Yufeng}, title = {Provably Size-Guaranteed Mesh Generation with Superconvergence}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2020}, volume = {17}, number = {2}, pages = {236--253}, abstract = {

The mesh conditions of high-quality grids generated by bubble placement method (BPM) and their superconvergence properties are studied in this paper. A mesh condition that for each pair of adjacent triangles, the lengths of any two opposite edges differ only by a high order of the parameter $h$ is derived. Furthermore, superconvergence estimations are analyzed on both linear and quadratic finite elements for elliptic boundary value problems under the above mesh condition. In particular, the mesh condition is found to be applicable to many known superconvergence estimations under different types of equations. Finally, numerical examples are presented to demonstrate the superconvergence properties on BPM-based grids.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/13649.html} }
TY - JOUR T1 - Provably Size-Guaranteed Mesh Generation with Superconvergence AU - Li , Xiangrong AU - Qi , Nan AU - Zhang , Weiwei AU - Nie , Yufeng JO - International Journal of Numerical Analysis and Modeling VL - 2 SP - 236 EP - 253 PY - 2020 DA - 2020/02 SN - 17 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/13649.html KW - Bubble placement method, mesh condition, superconvergence estimation. AB -

The mesh conditions of high-quality grids generated by bubble placement method (BPM) and their superconvergence properties are studied in this paper. A mesh condition that for each pair of adjacent triangles, the lengths of any two opposite edges differ only by a high order of the parameter $h$ is derived. Furthermore, superconvergence estimations are analyzed on both linear and quadratic finite elements for elliptic boundary value problems under the above mesh condition. In particular, the mesh condition is found to be applicable to many known superconvergence estimations under different types of equations. Finally, numerical examples are presented to demonstrate the superconvergence properties on BPM-based grids.

Xiangrong Li, Nan Qi, Weiwei Zhang & Yufeng Nie. (2020). Provably Size-Guaranteed Mesh Generation with Superconvergence. International Journal of Numerical Analysis and Modeling. 17 (2). 236-253. doi:
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