Displaying similar documents to “A class of nonparametric DSSY nonconforming quadrilateral elements”

Robust operator estimates and the application to substructuring methods for first-order systems

Christian Wieners, Barbara Wohlmuth (2014)

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

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We discuss a family of discontinuous Petrov–Galerkin (DPG) schemes for quite general partial differential operators. The starting point of our analysis is the DPG method introduced by [Demkowicz , 49 (2011) 1788–1809; Zitelli , 230 (2011) 2406–2432]. This discretization results in a sparse positive definite linear algebraic system which can be obtained from a saddle point problem by an element-wise Schur complement reduction applied to the test space. Here, we show that the abstract...

Optimal convergence rates of mortar finite element methods for second-order elliptic problems

Faker Ben Belgacem, Padmanabhan Seshaiyer, Manil Suri (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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We present an improved, near-optimal error estimate for a non-conforming finite element method, called the mortar method (M0). We also present a new mortaring technique, called the mortar method (MP), and derive , and error estimates for it, in the presence of quasiuniform and non-quasiuniform meshes. Our theoretical results, augmented by the computational evidence we present, show that like (M0), (MP) is also a viable mortaring technique for the method.

On Numerical Solution of the Gardner–Ostrovsky Equation

M. A. Obregon, Y. A. Stepanyants (2012)

Mathematical Modelling of Natural Phenomena

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A simple explicit numerical scheme is proposed for the solution of the Gardner–Ostrovsky equation ( + + + + ) = which is also known as the extended rotation-modified Korteweg–de Vries (KdV) equation. This equation is used for the description of internal oceanic waves affected by Earth’ rotation. Particular...

Risk bounds for new M-estimation problems

Nabil Rachdi, Jean-Claude Fort, Thierry Klein (2013)

ESAIM: Probability and Statistics

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In this paper, we consider a new framework where two types of data are available: experimental data supposed to be i.i.d from and outputs from a simulated reduced model. We develop a procedure for parameter estimation to characterize a feature of the phenomenon . We prove a risk bound qualifying the proposed procedure in terms of the number of experimental data , reduced model complexity...

Error Control and Andaptivity for a Phase Relaxation Model

Zhiming Chen, Ricardo H. Nochetto, Alfred Schmidt (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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The phase relaxation model is a diffuse interface model with small parameter which consists of a parabolic PDE for temperature and an ODE with double obstacles for phase variable . To decouple the system a semi-explicit Euler method with variable step-size is used for time discretization, which requires the stability constraint . Conforming piecewise linear finite elements over highly graded simplicial meshes with parameter are further employed for space discretization. error estimates...

Fixed-α and fixed-β efficiencies

Christopher S. Withers, Saralees Nadarajah (2013)

ESAIM: Probability and Statistics

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Consider testing :  ∈  against :  ∈  for a random sample , ..., from , where and are two disjoint sets of cdfs on ℝ = (−∞, ∞). Two non-local types of efficiencies, referred to as the fixed- and fixed- efficiencies, are introduced for this two-hypothesis testing situation. Theoretical tools are developed to evaluate these efficiencies for some of the most...

A posteriori error analysis for the Crank-Nicolson method for linear Schrödinger equations

Irene Kyza (2011)

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

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We prove error estimates of optimal order for linear Schrödinger-type equations in the ( )- and the ( )-norm. We discretize only in time by the Crank-Nicolson method. The direct use of the reconstruction technique, as it has been proposed by Akrivis in [ 75 (2006) 511–531], leads to upper bounds that are of optimal order in the ( )-norm, but of suboptimal order in the ( ...