Local problems on stars: a posteriori error estimators, convergence, and performance
Mathematics of Computation
On the a posteriori error analysis for equations of prescribed mean curvature
Mathematics of Computation
Convergence of an adaptive hp finite element strategy in one space dimension
Applied Numerical Mathematics
Journal of Computational and Applied Mathematics
Stopping Criterion for Adaptive Algorithm
ICCS '08 Proceedings of the 8th international conference on Computational Science, Part I
Schur complements on Hilbert spaces and saddle point systems
Journal of Computational and Applied Mathematics
Convergence analysis of an adaptive edge element method for Maxwell's equations
Applied Numerical Mathematics
Convergence of a standard adaptive nonconforming finite element method with optimal complexity
Applied Numerical Mathematics
Computational Optimization and Applications
A Convergent Nonconforming Adaptive Finite Element Method with Quasi-Optimal Complexity
SIAM Journal on Numerical Analysis
Convergence of an Adaptive Finite Element Method for Controlling Local Energy Errors
SIAM Journal on Numerical Analysis
Adaptive isogeometric analysis using rational PHT-splines
Computer-Aided Design
SIAM Journal on Numerical Analysis
Efficiency Based Adaptive Local Refinement for First-Order System Least-Squares Formulations
SIAM Journal on Scientific Computing
A Posteriori Error Control for Discontinuous Galerkin Methods for Parabolic Problems
SIAM Journal on Numerical Analysis
Convergence of an Adaptive Mixed Finite Element Method for Kirchhoff Plate Bending Problems
SIAM Journal on Numerical Analysis
Quasi-Optimality of Adaptive Nonconforming Finite Element Methods for the Stokes Equations
SIAM Journal on Numerical Analysis
Estimator reduction and convergence of adaptive BEM
Applied Numerical Mathematics
Multilevel discretization of symmetric saddle point systems without the discrete LBB condition
Applied Numerical Mathematics
Convergence of an adaptive hp finite element strategy in higher space-dimensions
Applied Numerical Mathematics
Weighted Marking for Goal-oriented Adaptive Finite Element Methods
SIAM Journal on Numerical Analysis
Advances in Computational Mathematics
Journal of Scientific Computing
Convergence and quasi-optimality of adaptive FEM with inhomogeneous Dirichlet data
Journal of Computational and Applied Mathematics
Computers & Mathematics with Applications
Multilevel Gradient Uzawa Algorithms for Symmetric Saddle Point Problems
Journal of Scientific Computing
Constraint-Free Adaptive FEMs on Quadrilateral Nonconforming Meshes
Journal of Scientific Computing
Computers & Mathematics with Applications
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Data oscillation is intrinsic information missed by the averaging process associated with finite element methods (FEM) regardless of quadrature. Ensuring a reduction rate of data oscillation, together with an error reduction based on a posteriori error estimators, we construct a simple and efficient adaptive FEM for elliptic partial differential equations (PDEs) with linear rate of convergence without any preliminary mesh adaptation nor explicit knowledge of constants. Any prescribed error tolerance is thus achieved in a finite number of steps. A number of numerical experiments in two and three dimensions yield quasi-optimal meshes along with a competitive performance.