A posteriori error estimates for the generalized Schwarz method of a new class of advection-diffusion equation with mixed boundary condition

2018 ◽  
Vol 41 (14) ◽  
pp. 5493-5505 ◽  
Author(s):  
Salah Boulaaras ◽  
Mohammed Said Touati Brahim ◽  
Smail Bouzenada
Keyword(s):  
Boundary Condition ◽  
Mixed Boundary Condition ◽  
Mixed Boundary ◽  
A Posteriori Error Estimates ◽  
Posteriori Error ◽  
A Posteriori ◽  
A Posteriori Error ◽  
New Class ◽  
Advection Diffusion Equation ◽  
Advection Diffusion

scholarly journals A posteriori error estimates for the generalized overlapping domain decomposition method for a parabolic variational equation with mixed boundary condition

2019 ◽  
Vol 38 (4) ◽  
pp. 111-126
Author(s):  
Salah Boulaaras ◽  
Khaled Habita ◽  
Mohamed Haiour
Keyword(s):  
Decomposition Method ◽  
Mixed Boundary Condition ◽  
Mixed Boundary ◽  
Variational Equation ◽  
Domain Decomposition Method ◽  
A Posteriori Error Estimates ◽  
Posteriori Error ◽  
A Posteriori ◽  
A Posteriori Error ◽  
Overlapping Domain Decomposition

The paper deals with a posteriori error estimates for the generalized overlapping domain decomposition method with mixed boundary condition the interfaces for parabolic variational equation with Laplace boundary value problems are proved using by the theta time scheme combined with Galerkin spatial approximation.

Effective Convergence Checks for Verifying Finite Element Stresses at Three-Dimensional Stress Concentrations

2018 ◽  
Vol 3 (3) ◽  
Author(s):  
J. R. Beisheim ◽  
G. B. Sinclair ◽  
P. J. Roache
Keyword(s):  
Finite Element ◽  
Error Estimation ◽  
A Posteriori Error Estimates ◽  
Three Dimensional ◽  
Posteriori Error ◽  
Test Problems ◽  
A Posteriori ◽  
Stress Concentrations ◽  
Element Analysis ◽  
A Posteriori Error

Current computational capabilities facilitate the application of finite element analysis (FEA) to three-dimensional geometries to determine peak stresses. The three-dimensional stress concentrations so quantified are useful in practice provided the discretization error attending their determination with finite elements has been sufficiently controlled. Here, we provide some convergence checks and companion a posteriori error estimates that can be used to verify such three-dimensional FEA, and thus enable engineers to control discretization errors. These checks are designed to promote conservative error estimation. They are applied to twelve three-dimensional test problems that have exact solutions for their peak stresses. Error levels in the FEA of these peak stresses are classified in accordance with: 1–5%, satisfactory; 1/5–1%, good; and <1/5%, excellent. The present convergence checks result in 111 error assessments for the test problems. For these 111, errors are assessed as being at the same level as true exact errors on 99 occasions, one level worse for the other 12. Hence, stress error estimation that is largely reasonably accurate (89%), and otherwise modestly conservative (11%).

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