Convergence of an adaptive hp finite element strategy in one space dimension
Applied Numerical 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 Convergent Nonconforming Adaptive Finite Element Method with Quasi-Optimal Complexity
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
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
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
The adaptive finite element method based on multi-scale discretizations for eigenvalue problems
Computers & Mathematics with Applications
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
Computers & Mathematics with Applications
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In this paper an adaptive finite element method is constructed for solving elliptic equations that has optimal computational complexity. Whenever, for some s 0, the solution can be approximated within a tolerance ε 0 in energy norm by a continuous piecewise linear function on some partition with O(ε-1/s) triangles, and one knows how to approximate the right-hand side in the dual norm with the same rate with piecewise constants, then the adaptive method produces approximations that converge with this rate, taking a number of operations that is of the order of the number of triangles in the output partition. The method is similar in spirit to that from [SINUM, 38 (2000), pp. 466-488] by Morin, Nochetto, and Siebert, and so in particular it does not rely on a recurrent coarsening of the partitions. Although the Poisson equation in two dimensions with piecewise linear approximation is considered, the results generalize in several respects.