scholarly journals An Optimal Error Estimates ofH1-Galerkin Expanded Mixed Finite Element Methods for Nonlinear Viscoelasticity-Type Equation

2011 ◽  
Vol 2011 ◽  
pp. 1-18 ◽  
Author(s):  
Haitao Che ◽  
Yiju Wang ◽  
Zhaojie Zhou
Keyword(s):  
Finite Element ◽  
Nonlinear Viscoelasticity ◽  
Mixed Finite Element ◽  
A Priori ◽  
Type Equation ◽  
Mixed Finite Element Method ◽  
Optimal Error Estimates ◽  
Uniqueness Of Solutions ◽  
Expanded Mixed Finite Element ◽  
Element Method

We investigate aH1-Galerkin mixed finite element method for nonlinear viscoelasticity equations based onH1-Galerkin method and expanded mixed element method. The existence and uniqueness of solutions to the numerical scheme are proved. A priori error estimation is derived for the unknown function, the gradient function, and the flux.

scholarly journals A New Positive Definite Expanded Mixed Finite Element Method for Parabolic Integrodifferential Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-24 ◽  
Author(s):  
Yang Liu ◽  
Hong Li ◽  
Jinfeng Wang ◽  
Wei Gao
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Mixed Finite Element ◽  
Mixed Finite Element Method ◽  
Positive Definite ◽  
Integrodifferential Equations ◽  
Fully Discrete ◽  
Mixed Scheme ◽  
Expanded Mixed Finite Element ◽  
Element Method

A new positive definite expanded mixed finite element method is proposed for parabolic partial integrodifferential equations. Compared to expanded mixed scheme, the new expanded mixed element system is symmetric positive definite and both the gradient equation and the flux equation are separated from its scalar unknown equation. The existence and uniqueness for semidiscrete scheme are proved and error estimates are derived for both semidiscrete and fully discrete schemes. Finally, some numerical results are provided to confirm our theoretical analysis.

scholarly journals Expanded Mixed Finite Element Method for the Two-Dimensional Sobolev Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Qing-li Zhao ◽  
Zong-cheng Li ◽  
You-zheng Ding
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Mixed Finite Element ◽  
Mixed Finite Element Method ◽  
Optimal Order ◽  
Two Dimensional ◽  
Sobolev Equation ◽  
Order Error ◽  
Expanded Mixed Finite Element ◽  
Element Method

Expanded mixed finite element method is introduced to approximate the two-dimensional Sobolev equation. This formulation expands the standard mixed formulation in the sense that three unknown variables are explicitly treated. Existence and uniqueness of the numerical solution are demonstrated. Optimal order error estimates for both the scalar and two vector functions are established.

A Stabilized Mixed Finite Element Method for Nearly Incompressible Elasticity

2005 ◽  
Vol 72 (5) ◽  
pp. 711-720 ◽  
Author(s):  
Arif Masud ◽  
Kaiming Xia
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Mixed Finite Element ◽  
A Priori ◽  
Mixed Finite Element Method ◽  
Element Formulation ◽  
Patch Tests ◽  
Stabilized Finite Element Method ◽  
Incompressible Elasticity ◽  
Element Method

We present a new multiscale/stabilized finite element method for compressible and incompressible elasticity. The multiscale method arises from a decomposition of the displacement field into coarse (resolved) and fine (unresolved) scales. The resulting stabilized-mixed form consistently represents the fine computational scales in the solution and thus possesses higher coarse mesh accuracy. The ensuing finite element formulation allows arbitrary combinations of interpolation functions for the displacement and stress fields. Specifically, equal order interpolations that are easy to implement but violate the celebrated Babushka-Brezzi inf-sup condition, become stable and convergent. Since the proposed framework is based on sound variational foundations, it provides a basis for a priori error analysis of the system. Numerical simulations pass various element patch tests and confirm optimal convergence in the norms considered.

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