scholarly journals An overlapping domain decomposition framework without dual formulation for variational imaging problems

2020 ◽  
Vol 46 (4) ◽  
Author(s):  
Jongho Park
Keyword(s):  
Domain Decomposition ◽  
Dual Formulation ◽  
Overlapping Domain Decomposition

scholarly journals A Posteriori Error Estimates for the Generalized Overlapping Domain Decomposition Methods

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Hakima Benlarbi ◽  
Ahmed-Salah Chibi
Keyword(s):  
Error Estimate ◽  
Domain Decomposition ◽  
Error Estimates ◽  
Domain Decomposition Method ◽  
A Posteriori Error Estimates ◽  
Posteriori Error ◽  
Decomposition Methods ◽  
A Posteriori ◽  
A Posteriori Error ◽  
Overlapping Domain Decomposition

A posteriori error estimates for the generalized overlapping domain decomposition method (GODDM) (i.e., with Robin boundary conditions on the interfaces), for second order boundary value problems, are derived. We show that the error estimate in the continuous case depends on the differences of the traces of the subdomain solutions on the interfaces. After discretization of the domain by finite elements we use the techniques of the residuala posteriorierror analysis to get ana posteriorierror estimate for the discrete solutions on subdomains. The results of some numerical experiments are presented to support the theory.

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