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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.

Recent Advances in Numerical Methods and Computational Mathematics

Theory, Algorithms, and Applications in Science and Engineering

Eds. Priya Nair, Hans Müller

This edited volume brings together contributions from world-leading researchers on the forefront of numerical analysis and computational mathematics. The book covers finite element methods, spectral methods, iterative solvers, and high-performance computing techniques, with applications spanning fluid dynamics, structural mechanics, and quantum systems.

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