A priori and a posteriori estimates of stabilized mixed finite volume methods for the incompressible flow arising in arteriosclerosis

2020 ◽  
Vol 363 ◽  
pp. 35-52 ◽  
Author(s):  
Jian Li ◽  
Feifei Jing ◽  
Zhangxin Chen ◽  
Xiaolin Lin
Keyword(s):  
Finite Volume ◽  
Incompressible Flow ◽  
A Priori ◽  
Finite Volume Methods ◽  
A Posteriori ◽  
A Posteriori Estimates

scholarly journals Cell Conservative Flux Recovery and A Posteriori Error Estimate of Vertex-Centered Finite Volume Methods

2013 ◽  
Vol 5 (05) ◽  
pp. 705-727 ◽  
Author(s):  
Long Chen ◽  
Ming Wang
Keyword(s):  
Finite Volume ◽  
Control Volume ◽  
Mixed Finite Element ◽  
Posteriori Error ◽  
Finite Volume Methods ◽  
Posteriori Error Estimate ◽  
Error Estimator ◽  
A Posteriori ◽  
Error Estimators ◽  
Conservative Flux

AbstractA cell conservative flux recovery technique is developed here for vertex-centered finite volume methods of second order elliptic equations. It is based on solving a local Neumann problem on each control volume using mixed finite element methods. The recovered flux is used to construct a constant freea posteriorierror estimator which is proven to be reliable and efficient. Some numerical tests are presented to confirm the theoretical results. Our method works for general order finite volume methods and the recovery-based and residual-baseda posteriorierror estimators is the first result ona posteriorierror estimators for high order finite volume methods.

A Priori and A Posteriori Estimates of Conforming and Mixed FEM for a Kirchhoff Equation of Elliptic Type

2017 ◽  
Vol 17 (2) ◽  
pp. 217-236 ◽  
Author(s):  
Asha K. Dond ◽  
Amiya K. Pani
Keyword(s):  
Finite Element ◽  
Convergence Rates ◽  
Mixed Finite Element ◽  
A Priori ◽  
Kirchhoff Equation ◽  
Helmholtz Decomposition ◽  
Elliptic Type ◽  
A Posteriori ◽  
A Posteriori Estimates ◽  
Expanded Mixed Finite Element

AbstractIn this article, a priori and a posteriori estimates of conforming and expanded mixed finite element methods for a Kirchhoff equation of elliptic type are derived. For the expanded mixed finite element method, a variant of Brouwer’s fixed point argument combined with a monotonicity argument yields the well-posedness of the discrete nonlinear system. Further, a use of both Helmholtz decomposition of $L^{2}$-vector valued functions and the discrete Helmholtz decomposition of the Raviart–Thomas finite elements helps in a crucial way to achieve optimal a priori as well as a posteriori error bounds. For both conforming and expanded mixed form, reliable and efficient a posteriori estimators are established. Finally, the numerical experiments are performed to validate the theoretical convergence rates.

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