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Residual and hierarchical a posteriori error estimates for nonconforming mixed finite element methods

Linda El Alaoui, Alexandre Ern (2004)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We analyze residual and hierarchical a posteriori error estimates for nonconforming finite element approximations of elliptic problems with variable coefficients. We consider a finite volume box scheme equivalent to a nonconforming mixed finite element method in a Petrov–Galerkin setting. We prove that all the estimators yield global upper and local lower bounds for the discretization error. Finally, we present results illustrating the efficiency of the estimators, for instance, in the simulation...

Residual and hierarchical a posteriori error estimates for nonconforming mixed finite element methods

Linda El Alaoui, Alexandre Ern (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We analyze residual and hierarchical a posteriori error estimates for nonconforming finite element approximations of elliptic problems with variable coefficients. We consider a finite volume box scheme equivalent to a nonconforming mixed finite element method in a Petrov–Galerkin setting. We prove that all the estimators yield global upper and local lower bounds for the discretization error. Finally, we present results illustrating the efficiency of the estimators, for instance, in the simulation...

Resolvent at low energy and Riesz transform for Schrödinger operators on asymptotically conic manifolds. II

Colin Guillarmou, Andrew Hassell (2009)

Annales de l’institut Fourier

Let M be a complete noncompact manifold of dimension at least 3 and g an asymptotically conic metric on M , in the sense that M compactifies to a manifold with boundary M so that g becomes a scattering metric on M . We study the resolvent kernel ( P + k 2 ) - 1 and Riesz transform T of the operator P = Δ g + V , where Δ g is the positive Laplacian associated to g and V is a real potential function smooth on M and vanishing at the boundary.In our first paper we assumed that P has neither zero modes nor a zero-resonance and showed...

Resonances and Spectral Shift Function near the Landau levels

Jean-François Bony, Vincent Bruneau, Georgi Raikov (2007)

Annales de l’institut Fourier

We consider the 3D Schrödinger operator H = H 0 + V where H 0 = ( - i - A ) 2 - b , A is a magnetic potential generating a constant magneticfield of strength b > 0 , and V is a short-range electric potential which decays superexponentially with respect to the variable along the magnetic field. We show that the resolvent of H admits a meromorphic extension from the upper half plane to an appropriate Riemann surface , and define the resonances of H as the poles of this meromorphic extension. We study their distribution near any fixed...

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