TY - JOUR
T1 - Error Estimates for the Laplace Interpolation on Convex Polygons
AU - Zhang , Weiwei
AU - Hu , Long
AU - Yang , Zongze
AU - Nie , Yufeng
JO - International Journal of Numerical Analysis and Modeling
VL - 3
SP - 324
EP - 338
PY - 2021
DA - 2021/03
SN - 18
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/18722.html
KW - Natural element method, geometric constraints, Laplace interpolation, error estimate.
AB - <p style="text-align: justify;">In the natural element method (NEM), the Laplace interpolation error estimate on
convex planar polygons is proved in this study. The proof is based on bounding gradients of the
Laplace interpolation for convex polygons which satisfy certain geometric requirements, and has
been divided into several parts that each part is bounded by a constant. Under the given geometric
assumptions, the optimal convergence estimate is obtained. This work provides the mathematical
analysis theory of the NEM. Some numerical examples are selected to verify our theoretical result.<br/></p>