Error estimates for the finite element solutions of variational inequalities
M. A. Noor, K. I. Noor (1983)
Annales Polonici Mathematici
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M. A. Noor, K. I. Noor (1983)
Annales Polonici Mathematici
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Sören Bartels (2010)
ESAIM: Mathematical Modelling and Numerical Analysis
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This article discusses the numerical approximation of time dependent Ginzburg-Landau equations. Optimal error estimates which are robust with respect to a large Ginzburg-Landau parameter are established for a semi-discrete in time and a fully discrete approximation scheme. The proofs rely on an asymptotic expansion of the exact solution and a stability result for degree-one Ginzburg-Landau vortices. The error bounds prove that degree-one vortices can be approximated robustly while...
Vejchodský, Tomáš
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This paper presents a review of the complementary technique with the emphasis on computable and guaranteed upper bounds of the approximation error. For simplicity, the approach is described on a numerical solution of the Poisson problem. We derive the complementary error bounds, prove their fundamental properties, present the method of hypercircle, mention possible generalizations and show a couple of numerical examples.
Olof Widlund (1977)
Publications mathématiques et informatique de Rennes
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Ned Anderson (1989)
Numerische Mathematik
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Stephen Wainger (1969-1970)
Séminaire de théorie des nombres de Bordeaux
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Segeth, Karel
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A lot of papers and books analyze analytical a posteriori error estimates from the point of view of robustness, guaranteed upper bounds, global efficiency, etc. At the same time, adaptive finite element methods have acquired the principal position among algorithms for solving differential problems in many physical and technical applications. In this survey contribution, we present and compare, from the viewpoint of adaptive computation, several recently published error estimation procedures...
S. Cochez-Dhondt, S. Nicaise, S. Repin (2009)
Mathematical Modelling of Natural Phenomena
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We present new a posteriori error estimates for the finite volume approximations of elliptic problems. They are obtained by applying functional a posteriori error estimates to natural extensions of the approximate solution and its flux computed by the finite volume method. The estimates give guaranteed upper bounds for the errors in terms of the primal (energy) norm, dual norm (for fluxes), and also in terms of the combined primal-dual norms. It is shown that the estimates provide sharp...
Friedhelm Schieweck (2010)
ESAIM: Mathematical Modelling and Numerical Analysis
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For a nonconforming finite element approximation of an elliptic model problem, we propose error estimates in the energy norm which use as an additive term the “post-processing error” between the original nonconforming finite element solution and an easy computable conforming approximation of that solution. Thus, for the error analysis, the existing theory from the conforming case can be used together with some simple additional arguments. As an essential point, the property is...
Gabriel N. Gatica (1987)
Extracta Mathematicae
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Yuping Zeng, Feng Wang (2017)
Applications of Mathematics
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We derive a residual-based a posteriori error estimator for a discontinuous Galerkin approximation of the Steklov eigenvalue problem. Moreover, we prove the reliability and efficiency of the error estimator. Numerical results are provided to verify our theoretical findings.
Teemu Luostari, Tomi Huttunen, Peter Monk (2013)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
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We prove error estimates for the ultra weak variational formulation (UWVF) in 3D linear elasticity. We show that the UWVF of Navier’s equation can be derived as an upwind discontinuous Galerkin method. Using this observation, error estimates are investigated applying techniques from the theory of discontinuous Galerkin methods. In particular, we derive a basic error estimate for the UWVF in a discontinuous Galerkin type norm and then an error estimate in the L() norm in terms of the...