A comparison of adaptive refinement techniques for elliptic problems
ACM Transactions on Mathematical Software (TOMS)
A convergent adaptive algorithm for Poisson's equation
SIAM Journal on Numerical Analysis
Data Oscillation and Convergence of Adaptive FEM
SIAM Journal on Numerical Analysis
Adaptive Finite Element Methods with convergence rates
Numerische Mathematik
An Optimal Adaptive Finite Element Method
SIAM Journal on Numerical Analysis
Convergence of Adaptive Finite Element Methods for General Second Order Linear Elliptic PDEs
SIAM Journal on Numerical Analysis
Optimality of a Standard Adaptive Finite Element Method
Foundations of Computational Mathematics
Convergence of Adaptive Discontinuous Galerkin Approximations of Second-Order Elliptic Problems
SIAM Journal on Numerical Analysis
Framework for the A Posteriori Error Analysis of Nonconforming Finite Elements
SIAM Journal on Numerical Analysis
An Optimal Adaptive Finite Element Method for the Stokes Problem
SIAM Journal on Numerical Analysis
An optimally convergent adaptive mixed finite element method
Numerische Mathematik
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In this paper, we prove convergence and quasi-optimal complexity of a simple adaptive nonconforming finite element method. In each step of the algorithm, the iterative solution of the discrete system is controlled by an adaptive stopping criterion, and the local refinement is based on either a simple edge residual or a volume term, depending on an adaptive marking strategy. We prove that this marking strategy guarantees a strict reduction of the error, augmented by the volume term and an additional oscillation term, and quasi-optimal complexity of the generated sequence of meshes.