Adaptive domain decomposition algorithms and finite volume/finite element approximation for advection-diffusion equations

1996 ◽  
Vol 11 (4) ◽  
pp. 299-341 ◽  
Author(s):  
M. C. Ciccoli
Keyword(s):  
Finite Element ◽  
Domain Decomposition ◽  
Finite Volume ◽  
Finite Element Approximation ◽  
Diffusion Equations ◽  
Element Approximation ◽  
Decomposition Algorithms ◽  
Advection Diffusion

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.

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