scholarly journals Parallel domain decomposition method for finite element approximation of 3D steady state non-Newtonian fluids

2015 ◽  
Vol 78 (8) ◽  
pp. 502-520 ◽  
Author(s):  
Wen-Shin Shiu ◽  
Feng-Nan Hwang ◽  
Xiao-Chuan Cai
Keyword(s):  
Finite Element ◽  
Steady State ◽  
Domain Decomposition ◽  
Decomposition Method ◽  
Domain Decomposition Method ◽  
Finite Element Approximation ◽  
Newtonian Fluids ◽  
Element Approximation

scholarly journals Numerical analysis of the mixed finite element method for the neutron diffusion eigenproblem with heterogeneous coefficients

2018 ◽  
Vol 52 (5) ◽  
pp. 2003-2035
Author(s):  
P. Ciarlet ◽  
L. Giret ◽  
E. Jamelot ◽  
F.D. Kpadonou
Keyword(s):  
Finite Element ◽  
Domain Decomposition ◽  
Decomposition Method ◽  
Source Term ◽  
Domain Decomposition Method ◽  
Mixed Finite Element ◽  
Mixed Finite Element Method ◽  
Finite Element Approximation ◽  
Element Approximation ◽  
Different Characteristics

We study first the convergence of the finite element approximation of the mixed diffusion equations with a source term, in the case where the solution is of low regularity. Such a situation commonly arises in the presence of three or more intersecting material components with different characteristics. Then we focus on the approximation of the associated eigenvalue problem. We prove spectral correctness for this problem in the mixed setting. These studies are carried out without, and then with a domain decomposition method. The domain decomposition method can be non-matching in the sense that the traces of the finite element spaces may not fit at the interface between subdomains. Finally, numerical experiments illustrate the accuracy of the method.

Simulation and computational heat transfer in the human eye with Dirichlet–Neumann domain decomposition approximation

2019 ◽  
Vol 10 (06) ◽  
pp. 1950041
Author(s):  
Salem Ahmedou Bamba ◽  
Abdellatif Ellabib
Keyword(s):  
Finite Element ◽  
Domain Decomposition ◽  
Domain Decomposition Method ◽  
Mathematical Formulation ◽  
Finite Element Approximation ◽  
Decomposition Methods ◽  
Element Approximation ◽  
Numerical Application ◽  
Human Eye ◽  
Uniqueness Of The Solution

In this paper, a bioheat model of temperature distribution in the human eye is studied, the mathematical formulation of this model is described using adequate mathematical tools. The existence and the uniqueness of the solution of this problem is proven and four algorithms based on finite element method approximation and domain decomposition methods are presented in details. The validation of all algorithm is done using a numerical application for an example where the analytical solution is known. The properties and parameters reported in the open literature for the human eye are used to approximate numerically the temperature for bioheat model by finite element approximation and nonoverlapping domain decomposition method. The obtained results that are verified using the experimental results recorded in the literature revealed a better accuracy by the use of algorithm proposed.

A NEW INTERFACE CEMENT EQUILIBRATED MORTAR (NICEM) METHOD WITH ROBIN INTERFACE CONDITIONS: THE P1 FINITE ELEMENT CASE

2013 ◽  
Vol 23 (12) ◽  
pp. 2253-2292 ◽  
Author(s):  
CAROLINE JAPHET ◽  
YVON MADAY ◽  
FREDERIC NATAF
Keyword(s):  
Finite Element ◽  
Error Analysis ◽  
Domain Decomposition ◽  
Decomposition Method ◽  
Domain Decomposition Method ◽  
Numerical Results ◽  
New Method ◽  
Interface Conditions ◽  
Well Posed

We design and analyze a new non-conforming domain decomposition method, named the NICEM method, based on Schwarz-type approaches that allows for the use of Robin interface conditions on non-conforming grids. The method is proven to be well posed. The error analysis is performed in 2D and in 3D for P1 elements. Numerical results in 2D illustrate the new method.

New Mixed Finite Element Formulations for Transient and Steady State Creep Problems

1989 ◽  
Vol 42 (11S) ◽  
pp. S150-S156
Author(s):  
Abimael F. D. Loula ◽  
Joa˜o Nisan C. Guerreiro
Keyword(s):  
Finite Element ◽  
Steady State ◽  
Mixed Finite Element ◽  
Finite Element Approximation ◽  
Steady State Creep ◽  
Element Approximation ◽  
New Approach ◽  
Finite Element Approximations ◽  
Transient Problems ◽  
Transient And Steady State

We apply the mixed Petrov–Galerkin formulation to construct finite element approximations for transient and steady-state creep problems. With the new approach we recover stability, convergence, and accuracy of some Galerkin unstable approximations. We also present the main results on the numerical analysis and error estimates of the proposed finite element approximation for the steady problem, and discuss the asymptotic behavior of the continuum and discrete transient problems.

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