scholarly journals Discontinuous Mixed Covolume Methods for Linear Parabolic Integrodifferential Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Ailing Zhu
Keyword(s):  
Error Analysis ◽  
Error Estimate ◽  
Optimal Order ◽  
Triangular Meshes ◽  
Element Space ◽  
Order Error ◽  
First Order ◽  
Fully Discrete ◽  
Mixed Element

The semidiscrete and fully discrete discontinuous mixed covolume schemes for the linear parabolic integrodifferential problems on triangular meshes are proposed. The error analysis of the semidiscrete and fully discrete discontinuous mixed covolume scheme is presented and the optimal order error estimate in discontinuousH(div)and first-order error estimate inL2are obtained with the lowest order Raviart-Thomas mixed element space.

scholarly journals Discontinuous Mixed Covolume Methods for Parabolic Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Ailing Zhu ◽  
Ziwen Jiang
Keyword(s):  
Error Analysis ◽  
Error Estimate ◽  
Error Estimates ◽  
Parabolic Problems ◽  
Optimal Order ◽  
Order Error ◽  
First Order ◽  
Fully Discrete ◽  
Optimal Order Error Estimates ◽  
Backward Euler

We present the semidiscrete and the backward Euler fully discrete discontinuous mixed covolume schemes for parabolic problems on triangular meshes. We give the error analysis of the discontinuous mixed covolume schemes and obtain optimal order error estimates in discontinuousHdivand first-order error estimate inL2.

scholarly journals Variational and numerical analysis of the Signorini′s contact problem in viscoplasticity with damage

2003 ◽  
Vol 2003 (2) ◽  
pp. 87-114 ◽  
Author(s):  
J. R. Fernández ◽  
M. Sofonea
Keyword(s):  
Contact Problem ◽  
Numerical Solutions ◽  
Mechanical Damage ◽  
Parabolic Type ◽  
Approximate Solutions ◽  
Damage Function ◽  
Optimal Order ◽  
Order Error ◽  
Fully Discrete ◽  
Solution Regularity

We consider the quasistatic Signorini′s contact problem with damage for elastic-viscoplastic bodies. The mechanical damage of the material, caused by excessive stress or strain, is described by a damage function whose evolution is modeled by an inclusion of parabolic type. We provide a variational formulation for the mechanical problem and sketch a proof of the existence of a unique weak solution of the model. We then introduce and study a fully discrete scheme for the numerical solutions of the problem. An optimal order error estimate is derived for the approximate solutions under suitable solution regularity. Numerical examples are presented to show the performance of the method.

scholarly journals The Convergence Ball and Error Analysis of the Relaxed Secant Method

2017 ◽  
Vol 2017 ◽  
pp. 1-7
Author(s):  
Rongfei Lin ◽  
Qingbiao Wu ◽  
Minhong Chen ◽  
Lu Liu
Keyword(s):  
Nonlinear Equation ◽  
Error Analysis ◽  
Error Estimate ◽  
Secant Method ◽  
Speed Of Convergence ◽  
Convergence Ball ◽  
Numerical Examples ◽  
Lipschitz Continuous ◽  
First Order ◽  
Nonlinear Equation Systems

A relaxed secant method is proposed. Radius estimate of the convergence ball of the relaxed secant method is attained for the nonlinear equation systems with Lipschitz continuous divided differences of first order. The error estimate is also established with matched convergence order. From the radius and error estimate, the relation between the radius and the speed of convergence is discussed with parameter. At last, some numerical examples are given.

scholarly journals Robust Calibration of Cameras with Telephoto Lens Using Regularized Least Squares

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Mingpei Liang ◽  
Xinyu Huang ◽  
Chung-Hao Chen ◽  
Gaolin Zheng ◽  
Alade Tokuta
Keyword(s):  
Error Analysis ◽  
Camera Calibration ◽  
Focal Length ◽  
Real Data ◽  
Order Error ◽  
First Order ◽  
Camera Parameters ◽  
The One ◽  
Well Posed ◽  
Telephoto Lens

Cameras with telephoto lens are usually used to recover details of an object that is either small or located far away from the cameras. However, the calibration of this kind of cameras is not as accurate as the one of cameras with short focal lengths that are commonly used in many vision applications. This paper has two contributions. First, we present a first-order error analysis that shows the relation between focal length and estimation uncertainties of camera parameters. To our knowledge, this error analysis with respect to focal length has not been studied in the area of camera calibration. Second, we propose a robust algorithm to calibrate the camera with a long focal length without using additional devices. By adding a regularization term, our algorithm makes the estimation of the image of the absolute conic well posed. As a consequence, the covariance of camera parameters can be reduced greatly. We further used simulations and real data to verify our proposed algorithm and obtained very stable results.

Stability and Error Analysis for the First-Order Euler Implicit/Explicit Scheme for the 3D MHD Equations

2017 ◽  
Vol 15 (01) ◽  
pp. 1750077 ◽  
Author(s):  
Jinjin Yang ◽  
Yinnian He
Keyword(s):  
Initial Data ◽  
Error Estimate ◽  
Stability Condition ◽  
Explicit Scheme ◽  
Mhd Equations ◽  
Discrete Solution ◽  
First Order ◽  
Fully Discrete ◽  
The Stability ◽  
Optimal Formula

This paper focuses on the stability and convergence analysis of the first-order Euler implicit/explicit scheme based on mixed finite element approximation for three-dimensional (3D) time-dependent MHD equations. Firstly, for initial data [Formula: see text] with [Formula: see text], the regularity results of the continuous solution [Formula: see text] and the spatial semi-discretization solution [Formula: see text] are obtained, and [Formula: see text]-error estimate of [Formula: see text] is deduced by using the negative norm technique. Next, through the use of mathematic induction, the [Formula: see text]-stability of the fully discrete first-order scheme is proved under the stability condition depending on the smoothness of initial data. Here, the stability condition is [Formula: see text] for [Formula: see text] and [Formula: see text] for [Formula: see text] where [Formula: see text] is some positive constant. Then, under the stability condition, the optimal [Formula: see text]-[Formula: see text] error estimate of the fully discrete solution [Formula: see text] and optimal [Formula: see text]-error estimate of the fully discrete solution [Formula: see text] are established by using the parabolic dual argument.

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