Explicit error bounds for the α-quasi-periodic Helmholtz problem [PDF]
, 2013 This paper considers a finite element approach to modeling electromagnetic waves in a periodic diffraction grating. In particular, an a priori error estimate associated with the α-quasi-periodic transformation is derived.
Mulholland, Anthony J., Lord, Natacha H.
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A priori error estimates for energy-based quasicontinuum approximations of a periodic chain [PDF]
, 2011 We derive a priori error estimates for three prototypical energy-based quasicontinuum (QC) methods: the local QC method, the energy-based QC method, and the quasi-nonlocal QC method.
Christoph Ortner +3 more
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Robust a priori and a posteriori error analysis for the approximation of Allen–Cahn and Ginzburg–Landau equations past topological changes [PDF]
, 2010 A priori and a posteriori error estimates are derived for the numerical approximation of scalar and complex valued phase field models. Particular attention is devoted to the dependence of the estimates on a small parameter and to the validity of the ...
Rüdiger Müller +11 more
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A priori error analysis of two force-based atomistic/continuum models of a periodic chain [PDF]
, 2011 The force-based quasicontinuum (QCF) approximation is a non-conservative atomistic/continuum hybrid model for the simulation of defects in crystals. We present an a priori error analysis of the QCF method, applied to a one-dimensional periodic chain ...
Makridakis , C. +9 more
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A priori and a posteriori analysis of the quasinonlocal quasicontinuum method in 1D [PDF]
, 2010 For a next-nearest neighbour pair interaction model in a periodic domain, a priori and a posteriori analyses of the quasinonlocal quasicontinuum method (QNL-QC) are presented.
Christoph Ortner, Ortner, Christoph
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A Priori Error Estimates for Mixed Finite Element Schemes for the Wave Equation
Sultan Qaboos University Journal for Science, 2015 A family of implicit-in-time mixed finite element schemes is presented for the numerical approximation of the acoustic wave equation. The mixed space discretization is based on the displacement form of the wave equation and the time-stepping method ...
Samir Karaa
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Error estimates of finite volume method for Stokes optimal control problem
Journal of Inequalities and Applications, 2021 In this paper, we discuss a priori error estimates for the finite volume element approximation of optimal control problem governed by Stokes equations. Under some reasonable assumptions, we obtain optimal L 2 $L^{2}$ -norm error estimates.
Lin Lan +4 more
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Analysis of an energy-based atomistic/continuum approximation of a vacancy in the 2D triangular lattice [PDF]
, 2013 We present an a priori error analysis of a practical energy based atomistic/continuum coupling method (A. V. Shapeev, Multiscale Model. Simul., 9(3):905-932, 2011) in two dimensions, for finite-range pair-potential interactions, in the presence of ...
Ortner, C. +2 more
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A posteriori error control for a quasi-continuum approximation of a periodic chain [PDF]
, 2013 We consider a one-dimensional periodic atomistic model, for which we formulate and analyse an adaptive variant of a quasicontinuum method. We establish a posteriori error estimators for the energy norm and for the energy, based on a posteriori residual ...
Wang, Hoa, Ortner, Christoph
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Error estimates of a semi-discrete LDG method for the system of damped acoustic wave equation
Advances in Difference Equations, 2018 We consider a system of acoustic wave equation possessing lower-order perturbation terms in a bounded domain in R2 $\mathbb{R}^{2}$. In this paper, we show the system is well-posed and stable with energy decays introducing a local discontinuous Galerkin (
Dojin Kim
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