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 - <p style="text-align: justify;">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.</p>