scholarly journals Maximum Norm Analysis of a Nonmatching Grids Method for Nonlinear Elliptic PDES

2011 ◽  
Vol 2011 ◽  
pp. 1-18 ◽  
Author(s):  
A. Harbi ◽  
M. Boulbrachene
Keyword(s):  
Exact Solution ◽  
Finite Element ◽  
The Other ◽  
Maximum Norm ◽  
Elliptic Pdes ◽  
Elliptic Pde ◽  
Schwarz Alternating Method ◽  
Nonmatching Grids ◽  
Nonlinear Elliptic ◽  
Mutually Independent

We provide a maximum norm analysis of a finite element Schwarz alternating method for a nonlinear elliptic PDE on two overlapping subdomains with nonmatching grids. We consider a domain which is the union of two overlapping subdomains where each subdomain has its own independently generated grid. The two meshes being mutually independent on the overlap region, a triangle belonging to one triangulation does not necessarily belong to the other one. Under a Lipschitz asssumption on the nonlinearity, we establish, on each subdomain, an optimalL∞error estimate between the discrete Schwarz sequence and the exact solution of the PDE.

scholarly journals The maximum norm analysis of a nonmatching grids method for a class of parabolic equation with nonlinear source terms

2019 ◽  
Vol 38 (4) ◽  
pp. 157-174 ◽  
Author(s):  
Salah Boulaaras ◽  
Mohammed Cherif Bahi ◽  
Mohamed Haiour ◽  
Abderrahman Zarai
Keyword(s):  
Parabolic Equation ◽  
The Other ◽  
Maximum Norm ◽  
Euler Scheme ◽  
Source Terms ◽  
Parabolic Differential Equations ◽  
Schwarz Alternating Method ◽  
Nonlinear Source ◽  
Nonmatching Grids ◽  
Mutually Independent

Motivated by the idea which has been introduced by M. Haiour and S.Boulaaras (Proc. Indian Acad. Sci. (Math. Sci.) Vol. 121,No. 4, November 2011,pp.481--493), We provide a maximum norm analysis of Euler scheme combined with finite element Schwarz alternating method for a class of parabolic equation with nonlinear source terms on two overlapping subdomains with nonmatching grids. We consider a domain which is the union of two overlapping subdomains where each subdomain has its own independently generated grid. The two meshes being mutually independent on the overlap region, a triangle belonging to one triangulation does not necessarily belong to the other one. Under a stability analysis on the theta scheme which given by our work in (App. Math. Comp., 217, 6443--6450 (2011).), we establish, on each subdomain, an optimal asymptotic behavior between the discrete Schwarz sequence and the asymptotic solution of parabolic differential equations.

scholarly journals Finite Element Convergence Analysis of a Schwarz Alternating Method for Nonlinear Elliptic PDEs

2020 ◽  
Vol 24 (2) ◽  
pp. 109
Author(s):  
Messaoud Boulbrachene
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Error Estimate ◽  
Elliptic Partial Differential Equations ◽  
Elliptic Pdes ◽  
Schwarz Alternating Method ◽  
Nonmatching Grids ◽  
Nonlinear Elliptic ◽  
Standard Finite Element Method ◽  
Linear Problems

In this paper, we prove uniform convergence of the standard finite element method for a Schwarz alternating procedure for nonlinear elliptic partial differential equations in the context of linear subdomain problems and nonmatching grids. The method stands on the combination of the convergence of linear Schwarz sequences with standard finite element  L-error estimate for linear problems.

scholarly journals The maximum norm analysis of a nonmatching grids method for a class of parabolic $p(x)$-Laplacien equation

2022 ◽  
Vol 40 ◽  
pp. 1-13
Author(s):  
Sadok Otmani ◽  
Salah Boulaaras ◽  
Ali Allahem
Keyword(s):  
Error Analysis ◽  
Continuous Solution ◽  
Maximum Norm ◽  
Optimal Error ◽  
Schwarz Alternating Method ◽  
Nonmatching Grids ◽  
Alternating Method

Motivated by the work of Boulaaras and Haiour in [7], we provide a maximum norm analysis of Schwarz alternating method for parabolic p(x)-Laplacien equation, where an optimal error analysis each subdomain between the discrete Schwarz sequence and the continuous solution of the presented problem is established

scholarly journals Finite element analysis of reinforced concrete deep beam with large opening

2021 ◽  
Vol 10 (1) ◽  
Author(s):  
Elsayed Ismail ◽  
Mohamed S. Issa ◽  
Khaled Elbadry
Keyword(s):  
Finite Element ◽  
Reinforced Concrete ◽  
Concrete Beams ◽  
Load Capacity ◽  
Reinforced Concrete Beams ◽  
The Other ◽  
Deep Beam ◽  
Web Openings ◽  
Design Load ◽  
Large Opening

Abstract Background A series of nonlinear finite element (FE) analyses was performed to evaluate the different design approaches available in the literature for design of reinforced concrete deep beam with large opening. Three finite element models were developed and analyzed using the computer software ATENA. The three FE models of the deep beams were made for details based on three different design approaches: (Kong, F.K. and Sharp, G.R., Magazine of Concrete Res_30:89-95, 1978), (Mansur, M. A., Design of reinforced concrete beams with web openings, 2006), and Strut and Tie method (STM) as per ACI 318-14 (ACI318 Committee, Building Code Requirements for Structural Concrete (ACI318-14), 2014). Results from the FE analyses were compared with the three approaches to evaluate the effect of different reinforcement details on the structural behavior of transfer deep beam with large opening. Results The service load deflection is the same for the three models. The stiffnesses of the designs of (Mansur, M. A., Design of reinforced concrete beams with web openings, 2006) and STM reduce at a load higher than the ultimate design load while the (Kong, F.K. and Sharp, G.R., Magazine of Concrete Res_30:89-95, 1978) reduces stiffness at a load close to the ultimate design load. The deep beam designed according to (Mansur, M. A., Design of reinforced concrete beams with web openings, 2006) model starts cracking at load higher than the beam designed according to (Kong, F.K. and Sharp, G.R., Magazine of Concrete Res_30:89-95, 1978) method. The deep beam detailed according to (Kong, F.K. and Sharp, G.R., Magazine of Concrete Res_30:89-95, 1978) and (Mansur, M. A., Design of reinforced concrete beams with web openings, 2006) failed due to extensive shear cracks. The specimen detailed according to STM restores its capacity after initial failure. The three models satisfy the deflection limit. Conclusion It is found that the three design approaches give sufficient ultimate load capacity. The amount of reinforcement given by both (Mansur, M. A., Design of reinforced concrete beams with web openings, 2006) and (Kong, F.K. and Sharp, G.R., Magazine of Concrete Res_30:89-95, 1978) is the same. The reinforcement used by the STM method is higher than the other two methods. Additional reinforcement is needed to limit the crack widths. (Mansur, M. A., Design of reinforced concrete beams with web openings, (2006)) method gives lesser steel reinforcement requirement and higher failure load compared to the other two methods.

Stress Analysis of Cement Concrete Pavement under Overweight Loads

2012 ◽  
Vol 446-449 ◽  
pp. 949-953
Author(s):  
Ya Ni Lu ◽  
Tao Li Xiao
Keyword(s):  
Finite Element ◽  
Regression Analysis ◽  
Finite Element Model ◽  
Element Model ◽  
Concrete Pavement ◽  
The Other ◽  
Tension Stress ◽  
Statistical Regression ◽  
Cement Concrete ◽  
Cement Concrete Pavement

Special load has produced serious damage to the concrete pavement because of the great gross weight and heavy axle load, but the present specification has not mentioned this kind of load. On this occasion, Several conditions of critical load are identified through ANSYS finite element model analysis and the formula through statistical regression analysis to the bottom maximum tension stress is drawn up. Which can not only guide the concrete pavement design under the special load but also the result may be referred by the other kinds of engineering.

Study of Oscillating Flow of Viscoelastic Fluid With the Fractional Maxwell Model

2008 ◽  
Vol 130 (4) ◽  
Author(s):  
Jiu-hong Jia ◽  
Hong-xing Hua
Keyword(s):  
Exact Solution ◽  
Petroleum Chemistry ◽  
Viscoelastic Fluid ◽  
Maxwell Model ◽  
The Other ◽  
Oscillating Flow ◽  
Model Parameters ◽  
Series Approximation ◽  
Phase Lags ◽  
Annular Effect

The oscillating flow of the viscoelastic fluid in cylindrical pipes has been applied in many fields, such as industries of petroleum, chemistry, and bioengineering. It is studied using the fractional derivative Maxwell model in this paper. The exact solution is obtained utilizing a simpler and more reasonable technique. According to this velocity solution, the time-velocity profile of one kind of viscoelastic fluid is analyzed. From analysis, it is found that the flow behaves like the Newton fluid when the oscillating frequency is low, and the flow reversal occurs when the oscillating frequency is high. Moreover, two series approximations for the velocity are obtained and analyzed for different model parameters. In one series approximation, the velocity is parabolic in profile, while in the other series approximation, the velocity presents three characteristics: (1) it is independent of radius and at the centerline is smaller than that of steady Poiseuille flow, (2) the phase lags about 90deg with respect to the imposed pressure gradient, and (3) the Richardson annular effect is found near the wall.

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