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Adaptive Finite Element Methods for Elliptic Partial Differential Equations
Sofia Petrova, Dmitri Volkov
In: Recent Advances in Numerical Methods and Computational Mathematics
We present a novel a posteriori error estimation framework for adaptive finite element methods applied to second-order elliptic PDEs. Our approach combines residual-based error indicators with hierarchical basis functions, achieving optimal convergence rates on both structured and unstructured meshes. Numerical experiments on benchmark problems confirm the efficiency and robustness of the proposed algorithm.