This work derives a posteriori error estimate of polygonal finite element methods based on Wachspress barycentric coordinates. In particular, we prove that the classical residual-based a posteriori error estimator is both an upper and lower bounds for the discretization error. The analysis relies a Scott-Zhang type interpolation and homogeneity arguments for rational functions on polygonal elements. Numerical experiments on square and L-shaped domains demonstrate the effectiveness of the adaptive algorithm.
@article{arxiv.2605.04805,
title = {An Adaptive Finite Element Method Based on Generalized Barycentric Coordinates},
author = {Yihui Zhou and Yuwen Li},
journal= {arXiv preprint arXiv:2605.04805},
year = {2026}
}