scholarly journals Coupled and decoupled stabilized mixed finite element methods for nonstationary dual‐porosity‐Stokes fluid flow model

2019 ◽  
Vol 120 (6) ◽  
pp. 803-833 ◽  
Author(s):  
Md. Abdullah Al Mahbub ◽  
Xiaoming He ◽  
Nasrin Jahan Nasu ◽  
Changxin Qiu ◽  
Haibiao Zheng
Keyword(s):  
Finite Element ◽  
Fluid Flow ◽  
Finite Element Methods ◽  
Flow Model ◽  
Mixed Finite Element ◽  
Mixed Finite Element Methods ◽  
Dual Porosity ◽  
Stokes Fluid ◽  
Stabilized Mixed Finite Element

scholarly journals Stabilized Mixed Finite Element Methods for Linear Elasticity on Simplicial Grids in ℝn

2017 ◽  
Vol 17 (1) ◽  
pp. 17-31 ◽  
Author(s):  
Long Chen ◽  
Jun Hu ◽  
Xuehai Huang
Keyword(s):  
Finite Element ◽  
Finite Element Methods ◽  
Linear Elasticity ◽  
Degrees Of Freedom ◽  
Mixed Finite Element ◽  
A Priori ◽  
Mixed Finite Element Methods ◽  
Interpolation Operators ◽  
Stabilization Technique ◽  
Stabilized Mixed Finite Element

AbstractIn this paper, we design two classes of stabilized mixed finite element methods for linear elasticity on simplicial grids. In the first class of elements, we use ${\boldsymbol{H}(\operatorname{div},\Omega;\mathbb{S})}$-${P_{k}}$ and ${\boldsymbol{L}^{2}(\Omega;\mathbb{R}^{n})}$-${P_{k-1}}$ to approximate the stress and displacement spaces, respectively, for ${1\leq k\leq n}$, and employ a stabilization technique in terms of the jump of the discrete displacement over the edges/faces of the triangulation under consideration; in the second class of elements, we use ${\boldsymbol{H}_{0}^{1}(\Omega;\mathbb{R}^{n})}$-${P_{k}}$ to approximate the displacement space for ${1\leq k\leq n}$, and adopt the stabilization technique suggested by Brezzi, Fortin, and Marini [19]. We establish the discrete inf-sup conditions, and consequently present the a priori error analysis for them. The main ingredient for the analysis are two special interpolation operators, which can be constructed using a crucial ${\boldsymbol{H}(\operatorname{div})}$ bubble function space of polynomials on each element. The feature of these methods is the low number of global degrees of freedom in the lowest order case. We present some numerical results to demonstrate the theoretical estimates.

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