An adaptive finite element method for linear elliptic problems
Kenneth Eriksson,Claes Johnson +1 more
TLDR
In this article, a methode adaptative d'elements finis, basee sur une estimation d'erreur optimale de norme maxima for les problemes elliptiques lineaires, is proposed.Abstract:
On propose une methode adaptative d'elements finis, basee sur une estimation d'erreur optimale de norme maxima pour les problemes elliptiques lineairesread more
Citations
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Journal ArticleDOI
An optimal control approach to a posteriori error estimation in finite element methods
Roland Becker,Rolf Rannacher +1 more
TL;DR: The ‘dual-weighted-residual method’ is introduced initially within an abstract functional analytic setting, and is then developed in detail for several model situations featuring the characteristic properties of elliptic, parabolic and hyperbolic problems.
Journal ArticleDOI
Introduction to Adaptive Methods for Differential Equations
TL;DR: The Differential Calculus can be solved by a common method (Gottfried Wilhelm von Leibniz, 1646-1719) as mentioned in this paper, which is known as the Differential Algorithm of this calculus.
Journal ArticleDOI
Adaptive finite element methods in computational mechanics
Claes Johnson,Peter Hansbo +1 more
TL;DR: In this article, a general approach to adaptivity for finite element methods is presented and applications to linear elasticity, non-linear elasto-plasticity and nonlinear conservation laws, including numerical results.
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Validation of A-Posteriori Error Estimators by Numerical Approach
TL;DR: In this article, a numerical methodology which determines the quality (or robustness) of a-posteriori error estimators for finite-element solutions of linear elliptic problems is described.
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A posteriori finite element bounds for linear-functional outputs of elliptic partial differential equations
TL;DR: A domain decomposition finite element technique for efficiently generating lower and upper bounds to outputs which are linear functionals of the solutions to symmetric or nonsymmetric second-order coercive linear partial differential equations in two space dimensions is presented.
References
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Book
Accuracy estimates and adaptive refinements in finite element computations
TL;DR: This book contains papers discussing the recent developments in adaptive methods and their applications, an area of finite elements methods applicable to the needs of civil engineering.
Journal ArticleDOI
Some Optimal Error Estimates for Piecewise Linear Finite Element Approximations
Rolf Rannacher,L. Ridgway Scott +1 more
TL;DR: In this paper, it was shown that the Ritz projection onto spaces of piecewise linear finite elements is bounded in the Sobolev space, Wl, for 2 - p < oc.
Journal ArticleDOI
An adaptive finite element procedure for compressible high speed flows
TL;DR: In this paper, a finite element-based solution procedure for high-speed inviscid compressible flow problems is described, which is computationally more efficient than the one-step Taylor-Galerkin approach and better suited for implementation on the modern generation of vector computers.
Journal ArticleDOI
Maximum norm estimates in the finite element method on plane polygonal domains. I
A. H. Schatz,L. B. Wahlbin +1 more
TL;DR: In this article, the authors considered the model Dirichlet problem on a plane polygonal domain and derived the rate of convergence estimates in the maximum norm, up to the boundary, are given locally.
Journal ArticleDOI
Error Estimates and Adaptive Time-Step Control for a Class of One-Step Methods for Stiff Ordinary Differential Equations
TL;DR: New optimal a priori error estimates for a class of implicit one-step methods for stiff ordinary differential equations obtained by using the discontinuous Galerkin method with piecewise polynomials of degree zero and one are proved.
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