An adaptive mixed finite element method for wind field adjustment
Advances in Engineering Software
Journal of Computational Physics
Adaptivity and computational complexity in the numerical solution of ODEs
Journal of Complexity
Analysis of a modified Schrödinger operator in 2D: Regularity, index, and FEM
Journal of Computational and Applied Mathematics
Convergence of adaptive finite element methods in computational mechanics
Applied Numerical Mathematics
Convergence analysis of an adaptive edge element method for Maxwell's equations
Applied Numerical Mathematics
Compressive Algorithms--Adaptive Solutions of PDEs and Variational Problems
Proceedings of the 13th IMA International Conference on Mathematics of Surfaces XIII
Convergence of a standard adaptive nonconforming finite element method with optimal complexity
Applied Numerical Mathematics
A posteriori error estimators for the first-order least-squares finite element method
Journal of Computational and Applied Mathematics
The numerical solution of obstacle problem by self adaptive finite element method
WSEAS Transactions on Mathematics
An efficient, reliable and robust error estimator for elliptic problems in R3
Applied Numerical Mathematics
A Posteriori Error Estimation Based on Potential and Flux Reconstruction for the Heat Equation
SIAM Journal on Numerical Analysis
Recovery-Based Error Estimators for Interface Problems: Mixed and Nonconforming Finite Elements
SIAM Journal on Numerical Analysis
Convergence of an Adaptive Finite Element Method for Controlling Local Energy Errors
SIAM Journal on Numerical Analysis
Flux Recovery and A Posteriori Error Estimators: Conforming Elements for Scalar Elliptic Equations
SIAM Journal on Numerical Analysis
Quasi-Optimal Convergence Rate of an Adaptive Discontinuous Galerkin Method
SIAM Journal on Numerical Analysis
SIAM Journal on Scientific Computing
An adaptive discontinuous finite volume method for elliptic problems
Journal of Computational and Applied Mathematics
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
Convergence of the discontinuous finite volume method for elliptic problems with minimal regularity
Journal of Computational and Applied Mathematics
On error estimator and adaptivity in the meshless Galerkin boundary node method
Computational Mechanics
The adaptive finite element method based on multi-scale discretizations for eigenvalue problems
Computers & Mathematics with Applications
Journal of Scientific Computing
Journal of Computational and Applied Mathematics
On Adaptive Eulerian---Lagrangian Method for Linear Convection---Diffusion Problems
Journal of Scientific Computing
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Adaptive finite element methods (FEMs) have been widely used in applications for over 20 years now. In practice, they converge starting from coarse grids, although no mathematical theory has been able to prove this assertion. Ensuring an error reduction rate based on a posteriori error estimators, together with a reduction rate of data oscillation (information missed by the underlying averaging process), we construct a simple and efficient adaptive FEM for elliptic partial differential equations. We prove that this algorithm converges with linear rate 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. Extensions to higher order elements and applications to saddle point problems are discussed as well.