Convergence of an adaptive hp finite element strategy in one space dimension
Applied Numerical Mathematics
A Posteriori Error Estimates for Parabolic Variational Inequalities
Journal of Scientific Computing
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
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
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
Geometrically Consistent Mesh Modification
SIAM Journal on Numerical Analysis
SIAM Journal on Scientific Computing
Adaptive Finite Element Methods on Quadrilateral Meshes without Hanging Nodes
SIAM Journal on Scientific Computing
An adaptive discontinuous finite volume method for elliptic problems
Journal of Computational and Applied Mathematics
SIAM Journal on Numerical Analysis
Continuous Mesh Framework Part II: Validations and Applications
SIAM Journal on Numerical Analysis
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
Convergence of adaptive BEM for some mixed boundary value problem
Applied Numerical Mathematics
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
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
On Adaptive Eulerian---Lagrangian Method for Linear Convection---Diffusion Problems
Journal of Scientific Computing
Computers & Mathematics with Applications
Constraint-Free Adaptive FEMs on Quadrilateral Nonconforming Meshes
Journal of Scientific Computing
Computers & Mathematics with Applications
Hi-index | 0.00 |
Adaptive Finite Element Methods for numerically solving elliptic equations are used often in practice. Only recently [12], [17] have these methods been shown to converge. However, this convergence analysis says nothing about the rates of convergence of these methods and therefore does, in principle, not guarantee yet any numerical advantages of adaptive strategies versus non-adaptive strategies. The present paper modifies the adaptive method of Morin, Nochetto, and Siebert [17] for solving the Laplace equation with piecewise linear elements on domains in ℝ2 by adding a coarsening step and proves that this new method has certain optimal convergence rates in the energy norm (which is equivalent to the H1 norm). Namely, it is shown that whenever s0 and the solution u is such that for each n≥1, it can be approximated to accuracy O(n−s) in the energy norm by a continuous, piecewise linear function on a triangulation with n cells (using complete knowledge of u), then the adaptive algorithm constructs an approximation of the same type with the same asymptotic accuracy while using only information gained during the computational process. Moreover, the number of arithmetic computations in the proposed method is also of order O(n) for each n≥1. The construction and analysis of this adaptive method relies on the theory of nonlinear approximation.