An Adaptive Finite Element Method Based on Generalized Barycentric Coordinates
Provides theoretical justification for adaptive mesh refinement in polygonal finite element methods, which is important for computational mechanics but is an incremental extension of existing residual-based error estimation techniques.
This work derives a posteriori error estimates for polygonal finite element methods using Wachspress coordinates, proving that the residual-based estimator provides both upper and lower bounds for discretization error. Numerical experiments on square and L-shaped domains confirm the effectiveness of the adaptive algorithm.
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.