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arXiv · 2605.04805

An Adaptive Finite Element Method Based on Generalized Barycentric Coordinates

Yihui Zhou·Yuwen Li
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Abstract

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.

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Yihui Zhou, Yuwen Li. 2026-05-06. An Adaptive Finite Element Method Based on Generalized Barycentric Coordinates. https://arxiv.org/abs/2605.04805

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