A priori error estimator of the generalized-? method for structural dynamics

2003 ◽  
Vol 57 (4) ◽  
pp. 537-554 ◽  
Author(s):  
Jintai Chung ◽  
Eun-Hyoung Cho ◽  
Keeyoung Choi
Keyword(s):  
Structural Dynamics ◽  
A Priori ◽  
Error Estimator

scholarly journals A priori and a posteriori error analysis for a hybrid formulation of a prestressed shell model.

2021 ◽  
Author(s):  
Serge Nicaise ◽  
Ismail Merabet ◽  
Rayhana REZZAG BARA
Keyword(s):  
Shell Model ◽  
A Priori ◽  
Functional Space ◽  
Finite Element Approximation ◽  
Posteriori Error ◽  
Error Estimator ◽  
Element Approximation ◽  
A Posteriori ◽  
A Posteriori Error ◽  
A Priori Error Estimate

This work deals with the finite element approximation of a prestressed shell model using a new formulation where the unknowns (the displacement and the rotation of fibers normal to the midsurface) are described in Cartesian and local covariant basis respectively. Due to the constraint involved in the definition of the functional space, a penalized version is then considered. We obtain a non robust a priori error estimate of this penalized formulation, but a robust one is obtained for its mixed formulation. Moreover, we present a reliable and efficient a posteriori error estimator of the penalized formulation. Numerical tests are included that confirmthe efficiency of our residual a posteriori estimator.

scholarly journals Divergence-conforming discontinuous Galerkin finite elements for Stokes eigenvalue problems

2019 ◽  
Vol 144 (3) ◽  
pp. 585-614
Author(s):  
Joscha Gedicke ◽  
Arbaz Khan
Keyword(s):  
Discontinuous Galerkin ◽  
Eigenvalue Problems ◽  
Convergence Rates ◽  
A Priori ◽  
Posteriori Error ◽  
Error Estimator ◽  
A Posteriori ◽  
A Posteriori Error Estimator ◽  
Posteriori Error Estimator ◽  
A Posteriori Error

AbstractIn this paper, we present a divergence-conforming discontinuous Galerkin finite element method for Stokes eigenvalue problems. We prove a priori error estimates for the eigenvalue and eigenfunction errors and present a residual based a posteriori error estimator. The a posteriori error estimator is proven to be reliable and (locally) efficient. We finally present some numerical examples that verify the a priori convergence rates and the reliability and efficiency of the residual based a posteriori error estimator.

scholarly journals An Updating Method for Structural Dynamics Models with Uncertainties

2008 ◽  
Vol 15 (3-4) ◽  
pp. 245-256 ◽  
Author(s):  
B. Faverjon ◽  
P. Ladevèze ◽  
F. Louf
Keyword(s):  
Structural Dynamics ◽  
Polynomial Chaos ◽  
Error Estimator ◽  
Chaos Expansion ◽  
Finite Element Analyses ◽  
Industrial Structures ◽  
Stochastic Problems ◽  
Constitutive Relation Error ◽  
Dynamics Models

One challenge in the numerical simulation of industrial structures is model validation based on experimental data. Among the indirect or parametric methods available, one is based on the “mechanical” concept of constitutive relation error estimator introduced in order to quantify the quality of finite element analyses. In the case of uncertain measurements obtained from a family of quasi-identical structures, parameters need to be modeled randomly. In this paper, we consider the case of a damped structure modeled with stochastic variables. Polynomial chaos expansion and reduced bases are used to solve the stochastic problems involved in the calculation of the error.

Error-Controlled Model Reduction in Flexible Multibody Dynamics

2010 ◽  
Vol 5 (3) ◽  
Author(s):  
Jörg Fehr ◽  
Peter Eberhard
Keyword(s):  
Model Reduction ◽  
Error Bounds ◽  
Degrees Of Freedom ◽  
A Priori ◽  
Reduction Process ◽  
Flexible Multibody Dynamics ◽  
Scanning Tunneling ◽  
Error Estimator ◽  
Gramian Matrix ◽  
Flexible Multibody

One important issue for the simulation of flexible multibody systems is the quality controlled reduction in the flexible bodies degrees of freedom. In this work, the procedure is based on knowledge about the error induced by model reduction. For modal reduction, no error bound is available. For Gramian matrix based reduction methods, analytical error bounds can be developed. However, due to numerical reasons, the dominant eigenvectors of the Gramian matrix have to be approximated. Within this paper, two different methods are presented for this purpose. For moment matching methods, the development of a priori error bounds is still an active field of research. In this paper, an error estimator based on a new second order adaptive global Arnoldi algorithm is introduced and further assists the user in the reduction process. We evaluate and compare those methods by reducing the flexible degrees of freedom of a rack used for active vibration damping of a scanning tunneling microscope.

Comparing of Direct and Sensitivity-Base Model Updating Methods in Structural Dynamics and Its Application for Updating of Cantilever Model

2008 ◽  
Author(s):  
K. Abasi ◽  
M. Asayesh ◽  
M. Nikravesh
Keyword(s):  
Structural Dynamics ◽  
Model Updating ◽  
A Priori ◽  
Physical Parameters ◽  
Fe Model ◽  
Structural Components ◽  
Modal Data ◽  
Fe Model Updating ◽  
Fixed Boundary Condition ◽  
Small Rotation

Reliable finite element (FE) modeling in structural dynamics is very important for studies related to the safety of structural components used in industry. FE model updating is a tool to produce these reliable models. The method uses an initial FE model and experimental modal data of the structural components to modify physical parameters of the initial FE model, and a number of approaches have been developed to perform this task. This paper presents an overview of model updating and particularly its application for updating of cantilever model. An example of the need for model updating is a cantilever beam, where often the beam is assumed to be rigidly fixed at the clamped end. However, during tests it is often found that the beam has either a small rotation or deflection at the clamped end. If one has to construct the FE model without the knowledge of the experimental modal data, the natural assumption would be to include an ideal, fixed boundary condition, which may not be true. Even with such a simple structure the FE model is not reliable a priori, and based on intuition or engineering judgments it is difficult to estimate the values of the boundary stiffnesses. However, after creating an initial FE model, the model should be updated based on the experimental modal data obtained from modal tests so that the FE model may be used with confidence for further analysis.

A Priori and a Posteriori Error Estimates for H(div)-Elliptic Problem with Interior Penalty Method

2013 ◽  
Vol 14 (3) ◽  
pp. 753-779
Author(s):  
Yuping Zeng ◽  
Jinru Chen
Keyword(s):  
Elliptic Problem ◽  
A Priori ◽  
A Posteriori Error Estimates ◽  
Posteriori Error ◽  
Energy Norm ◽  
Error Estimator ◽  
A Posteriori ◽  
Interior Penalty ◽  
A Posteriori Error ◽  
A Priori Error Estimate

AbstractIn this paper, we propose and analyze the interior penalty discontinuous Galerkin method for H(div)-elliptic problem. An optimal a priori error estimate in the energy norm is proved. In addition, a residual-based a posteriori error estimator is obtained. The estimator is proved to be both reliable and efficient in the energy norm. Some numerical testes are presented to demonstrate the effectiveness of our method.

A STABILIZED SCHEME FOR THE LAGRANGE MULTIPLIER METHOD FOR ADVECTION-DIFFUSION EQUATIONS

2004 ◽  
Vol 14 (07) ◽  
pp. 1035-1060 ◽  
Author(s):  
GERD RAPIN ◽  
GERT LUBE
Keyword(s):  
A Priori ◽  
A Priori Estimate ◽  
Weak Sense ◽  
Posteriori Error ◽  
Diffusion Equations ◽  
Error Estimator ◽  
Posteriori Error Estimator ◽  
Stabilized Finite Element ◽  
Stabilized Finite Element Method ◽  
Advection Diffusion

We consider a new stabilized finite element method for advection-diffusion equations, where the Dirichlet boundary condition is imposed in a weak sense by Lagrange multipliers. The inf–sup condition of the corresponding mixed problem is circumvented by adding some further terms. Using the SUPG-stabilization, an optimal a priori estimate is shown for the singularly perturbed case. Then we present an a posteriori error estimator for our stabilized scheme. Some numerical experiments support the theoretical results. The present results are basic for a nonconforming three-field formulation of the problem.

scholarly journals Spectral Method with the Tensor-Product Nodal Basis for the Steklov Eigenvalue Problem

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Xuqing Zhang ◽  
Yidu Yang ◽  
Hai Bi
Keyword(s):  
Eigenvalue Problem ◽  
Tensor Product ◽  
Spectral Method ◽  
A Priori ◽  
Error Estimator ◽  
Steklov Eigenvalue ◽  
Steklov Eigenvalue Problem ◽  
Efficient Scheme ◽  
A Posterior Error ◽  
Nodal Basis

This paper discusses spectral method with the tensor-product nodal basis at the Legendre-Gauss-Lobatto points for solving the Steklov eigenvalue problem. A priori error estimates of spectral method are discussed, and based on the work of Melenk and Wohlmuth (2001), a posterior error estimator of the residual type is given and analyzed. In addition, this paper combines the shifted-inverse iterative method and spectral method to establish an efficient scheme. Finally, numerical experiments with MATLAB program are reported.

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