scholarly journals On an unconditionally convergent stabilized finite element approximation of resistive magnetohydrodynamics

2013 ◽  
Vol 234 ◽  
pp. 399-416 ◽  
Author(s):  
Santiago Badia ◽  
Ramon Codina ◽  
Ramon Planas
Keyword(s):  
Finite Element ◽  
Finite Element Approximation ◽  
Element Approximation ◽  
Stabilized Finite Element

scholarly journals Analysis of a stabilized finite element approximation for a linearized logarithmic reformulation of the viscoelastic flow problem

2020 ◽  
Author(s):  
Ramon Codina ◽  
Laura Moreno
Keyword(s):  
Finite Element ◽  
Flow Problem ◽  
Finite Element Approximation ◽  
Viscoelastic Flow ◽  
Element Approximation ◽  
Element Formulation ◽  
Stabilized Finite Element ◽  
Linearized Problem ◽  
Conformation Tensor ◽  
The Stability

In this paper we present the numerical analysis of a finite element method for a linearized viscoelastic flow problem. In particular, we analyze a linearization of the logarithmic reformulation of the problem, which in particular should be able to produce results for Weissenberg numbers higher than the standard one. In order to be able to use the same interpolation for all the unknowns (velocity, pressure and logarithm of the conformation tensor), we employ a stabilized finite element formulation based on the Variational Multi-Scale concept. The study of the linearized problem already serves to show why the logarithmic reformulation performs better than the standard one for high Weissenberg numbers; this is reflected in the stability and error estimates that we provide in this paper.

scholarly journals Fully Discrete Finite Element Methods for Two-Dimensional Bingham Flows

2018 ◽  
Vol 2018 ◽  
pp. 1-13
Author(s):  
Cheng Fang ◽  
Yuan Li
Keyword(s):  
Finite Element ◽  
Finite Element Methods ◽  
Piecewise Linear ◽  
Finite Element Approximation ◽  
Element Approximation ◽  
Two Dimensional ◽  
Stabilized Finite Element ◽  
Fully Discrete ◽  
Stabilized Finite Element Method ◽  
Discrete Finite Element

This paper presents fully discrete stabilized finite element methods for two-dimensional Bingham fluid flow based on the method of regularization. Motivated by the Brezzi-Pitkäranta stabilized finite element method, the equal-order piecewise linear finite element approximation is used for both the velocity and the pressure. Based on Euler semi-implicit scheme, a fully discrete scheme is introduced. It is shown that the proposed fully discrete stabilized finite element scheme results in the h1/2 error order for the velocity in the discrete norms corresponding to L2(0,T;H1(Ω)2)∩L∞(0,T;L2(Ω)2).

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