scholarly journals Error estimates for the unilateral buckling load of a plate involving the membrane efforts consistency error

2008 ◽  
pp. 1003-1038
Author(s):  
Mekki Ayadi
Keyword(s):  
Finite Elements ◽  
Error Estimate ◽  
Critical Load ◽  
Error Estimates ◽  
Thin Plate ◽  
Numerical Experiments ◽  
Mesh Size ◽  
Buckling Load ◽  
Plate Model ◽  
Consistency Error

The paper deals with error estimates for the unilateral buckling critical load of a thin plate in presence of an obstacle. The error on the membrane efforts tensor is taken into account. First, using the Mindlin’s plate model together with a finite elements scheme of degree one, an error estimate, depending on the mesh size h, is established. In order to validate this theoretical error estimate, some numerical experiments are presented. Second, using the Kirchhoff-Love’s plate model, an abstract error estimate is achieved. Its drawback is that it contains a hard term to evaluate.

scholarly journals Error estimates for the unilateral buckling critical load of a thin plate

2007 ◽  
pp. 583-600
Author(s):  
Mekki Ayadi
Keyword(s):  
Finite Elements ◽  
Error Estimate ◽  
Critical Load ◽  
Error Estimates ◽  
Thin Plate ◽  
Mesh Size ◽  
Numerical Results ◽  
Plate Model

The paper deals with error estimates for the unilateral buckling critical load of a thin plate in presence of an obstacle. First, using the Kirchhoff-Love’s plate model, an abstract error estimate is given up. Its drawback is that it contains a hard term to evaluate. Then, by using the Mindlin’s plate model together with a finite elements scheme of degree one, an error estimate, depending on the mesh size h, is established. The last part of the paper is devoted to some numerical results in order to validate the error estimate formula.

QMC integration errors and quasi-asymptotics

2020 ◽  
Vol 26 (3) ◽  
pp. 171-176
Author(s):  
Ilya M. Sobol ◽  
Boris V. Shukhman
Keyword(s):  
Monte Carlo ◽  
Error Estimate ◽  
Numerical Experiments ◽  
Probable Error ◽  
Quasi Monte Carlo ◽  
Integration Error ◽  
Asymptotic Error ◽  
Dimensional Cube ◽  
Integration Errors ◽  
Mc Method

AbstractA crude Monte Carlo (MC) method allows to calculate integrals over a d-dimensional cube. As the number N of integration nodes becomes large, the rate of probable error of the MC method decreases as {O(1/\sqrt{N})}. The use of quasi-random points instead of random points in the MC algorithm converts it to the quasi-Monte Carlo (QMC) method. The asymptotic error estimate of QMC integration of d-dimensional functions contains a multiplier {1/N}. However, the multiplier {(\ln N)^{d}} is also a part of the error estimate, which makes it virtually useless. We have proved that, in the general case, the QMC error estimate is not limited to the factor {1/N}. However, our numerical experiments show that using quasi-random points of Sobol sequences with {N=2^{m}} with natural m makes the integration error approximately proportional to {1/N}. In our numerical experiments, {d\leq 15}, and we used {N\leq 2^{40}} points generated by the SOBOLSEQ16384 code published in 2011. In this code, {d\leq 2^{14}} and {N\leq 2^{63}}.

scholarly journals A stabilized coupled method and its optimal error estimates for elliptic interface problems

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Jiaping Yu ◽  
Feng Shi ◽  
Jianping Zhao
Keyword(s):  
Error Estimates ◽  
Numerical Experiments ◽  
Interface Problems ◽  
Optimal Error Estimates ◽  
Computational Stability ◽  
Optimal Error ◽  
Stabilized Method ◽  
Elliptic Interface Problems ◽  
Coupled Method

Abstract In this paper, we present a stabilized coupled algorithm for solving elliptic interface problems, mainly by introducing the jump of the solutions along the interface. A framework of theoretical proofs is provided to show the optimal error estimates of this stabilized method. Several numerical experiments are carried out to demonstrate the computational stability and effectiveness of the method.

scholarly journals Least-Squares Estimators of Drift Parameter for Discretely Observed Fractional Ornstein–Uhlenbeck Processes

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 716 ◽  
Author(s):  
Pavel Kříž ◽  
Leszek Szała
Keyword(s):  
Brownian Motion ◽  
Least Squares ◽  
Fractional Brownian Motion ◽  
Numerical Experiments ◽  
Covariance Structure ◽  
Mesh Size ◽  
Uhlenbeck Process ◽  
Least Squares Estimators ◽  
Discrete Time Observations ◽  
Drift Parameter

We introduce three new estimators of the drift parameter of a fractional Ornstein–Uhlenbeck process. These estimators are based on modifications of the least-squares procedure utilizing the explicit formula for the process and covariance structure of a fractional Brownian motion. We demonstrate their advantageous properties in the setting of discrete-time observations with fixed mesh size, where they outperform the existing estimators. Numerical experiments by Monte Carlo simulations are conducted to confirm and illustrate theoretical findings. New estimation techniques can improve calibration of models in the form of linear stochastic differential equations driven by a fractional Brownian motion, which are used in diverse fields such as biology, neuroscience, finance and many others.

scholarly journals Oscillating behaviour of the spectrum for a plasmonic problem in a domain with a rounded corner

2018 ◽  
Vol 52 (4) ◽  
pp. 1285-1313 ◽  
Author(s):  
Lucas Chesnel ◽  
Xavier Claeys ◽  
Sergei A. Nazarov
Keyword(s):  
Asymptotic Expansion ◽  
Eigenvalue Problem ◽  
Recent Work ◽  
Present Article ◽  
Error Estimates ◽  
Numerical Experiments ◽  
Source Term ◽  
Oscillatory Behaviour ◽  
Time Harmonic ◽  
Rounded Corner

We investigate the eigenvalue problem −div(σ∇u) = λu (P) in a 2D domain Ω divided into two regions Ω±. We are interested in situations where σ takes positive values on Ω+ and negative ones on Ω−. Such problems appear in time harmonic electromagnetics in the modeling of plasmonic technologies. In a recent work [L. Chesnel, X. Claeys and S.A. Nazarov, Asymp. Anal. 88 (2014) 43–74], we highlighted an unusual instability phenomenon for the source term problem associated with (P): for certain configurations, when the interface between the subdomains Ω± presents a rounded corner, the solution may depend critically on the value of the rounding parameter. In the present article, we explain this property studying the eigenvalue problem (P). We provide an asymptotic expansion of the eigenvalues and prove error estimates. We establish an oscillatory behaviour of the eigenvalues as the rounding parameter of the corner tends to zero. We end the paper illustrating this phenomenon with numerical experiments.

scholarly journals On well-posedness of time-harmonic problems in an unbounded strip for a thin plate model

2019 ◽  
Vol 17 (6) ◽  
pp. 1487-1529 ◽  
Author(s):  
Laurent Bourgeois ◽  
Lucas Chesnel ◽  
Sonia Fliss
Keyword(s):  
Thin Plate ◽  
Well Posedness ◽  
Plate Model ◽  
Time Harmonic

scholarly journals A Posteriori Error Estimates for the Generalized Overlapping Domain Decomposition Methods

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Hakima Benlarbi ◽  
Ahmed-Salah Chibi
Keyword(s):  
Error Estimate ◽  
Domain Decomposition ◽  
Error Estimates ◽  
Domain Decomposition Method ◽  
A Posteriori Error Estimates ◽  
Posteriori Error ◽  
Decomposition Methods ◽  
A Posteriori ◽  
A Posteriori Error ◽  
Overlapping Domain Decomposition

A posteriori error estimates for the generalized overlapping domain decomposition method (GODDM) (i.e., with Robin boundary conditions on the interfaces), for second order boundary value problems, are derived. We show that the error estimate in the continuous case depends on the differences of the traces of the subdomain solutions on the interfaces. After discretization of the domain by finite elements we use the techniques of the residuala posteriorierror analysis to get ana posteriorierror estimate for the discrete solutions on subdomains. The results of some numerical experiments are presented to support the theory.

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