scholarly journals Maximum Norm Analysis of an Arbitrary Number of Nonmatching Grids Method for Nonlinears Elliptic PDES

2013 ◽  
Vol 2013 ◽  
pp. 1-21 ◽  
Author(s):  
Abida Harbi
Keyword(s):  
Arbitrary Number ◽  
Maximum Norm ◽  
Elliptic Pdes ◽  
Nonmatching Grids

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 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 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.

Kinematic analysis and deformation of a planar lattice with an arbitrary number of panels

2020 ◽  
pp. 15-19
Author(s):  
M.N. Kirsanov
Keyword(s):  
Exact Solution ◽  
Kinematic Analysis ◽  
Arbitrary Number ◽  
Design Parameters ◽  
Lattice Deformation ◽  
Planar Lattice ◽  
Force Loading

Formulae are obtained for calculating the deformations of a statically determinate lattice under the action of two types of loads in its plane, depending on the number of panels located along one side of the lattice. Two options for fixing the lattice are analyzed. Cases of kinematic variability of the structure are found. The distribution of forces in the rods of the lattice is shown. The dependences of the force loading of some rods on the design parameters are obtained. Keywords: truss, lattice, deformation, exact solution, deflection, induction, Maple system. [email protected]

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