scholarly journals A priori error estimates of fully discrete finite element Galerkin method for Kelvin–Voigt viscoelastic fluid flow model

2019 ◽  
Vol 78 (12) ◽  
pp. 3872-3895
Author(s):  
Saumya Bajpai ◽  
Ambit K. Pany
Keyword(s):  
Finite Element ◽  
Fluid Flow ◽  
Galerkin Method ◽  
Error Estimates ◽  
Flow Model ◽  
A Priori ◽  
Fully Discrete ◽  
Finite Element Galerkin Method ◽  
Priori Error Estimates ◽  
Discrete Finite Element

A MFE method combined with L1-approximation for a nonlinear time-fractional coupled diffusion system

2017 ◽  
Vol 08 (01) ◽  
pp. 1750012 ◽  
Author(s):  
Yaxin Hou ◽  
Ruihan Feng ◽  
Yang Liu ◽  
Hong Li ◽  
Wei Gao
Keyword(s):  
Finite Element ◽  
Mixed Finite Element ◽  
A Priori ◽  
Diffusion System ◽  
Fully Discrete ◽  
Coupled Diffusion ◽  
L1 Approximation ◽  
Priori Error Estimates ◽  
The Stability ◽  
Discrete Finite Element

In this paper, a nonlinear time-fractional coupled diffusion system is solved by using a mixed finite element (MFE) method in space combined with L1-approximation and implicit second-order backward difference scheme in time. The stability for nonlinear fully discrete finite element scheme is analyzed and a priori error estimates are derived. Finally, some numerical tests are shown to verify our theoretical analysis.

scholarly journals Convergence Analysis of H(div)-Conforming Finite Element Methods for a Nonlinear Poroelasticity Problem

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Yuping Zeng ◽  
Zhifeng Weng ◽  
Fen Liang
Keyword(s):  
Finite Element ◽  
Finite Element Methods ◽  
A Priori ◽  
Mixed Finite Elements ◽  
Elastic Displacement ◽  
Fully Discrete ◽  
Conforming Finite Element ◽  
Priori Error Estimates ◽  
Galerkin Formulation ◽  
Flow Variables

In this paper, we introduce and analyze H(div)-conforming finite element methods for a nonlinear model in poroelasticity. More precisely, the flow variables are discretized by H(div)-conforming mixed finite elements, while the elastic displacement is approximated by the H(div)-conforming finite element with the interior penalty discontinuous Galerkin formulation. Optimal a priori error estimates are derived for both semidiscrete and fully discrete schemes.

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