The optimal order convergence for the lowest order mixed finite element method of the biharmonic eigenvalue problem

2022 ◽  
Vol 402 ◽  
pp. 113783
Author(s):  
Jian Meng ◽  
Liquan Mei
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Eigenvalue Problem ◽  
Mixed Finite Element ◽  
Mixed Finite Element Method ◽  
Optimal Order ◽  
Order Convergence ◽  
Optimal Order Convergence ◽  
Element Method

scholarly journals A Framework for Nonconforming Mixed Finite Element Method for Elliptic Problems in ℝ3

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Gwanghyun Jo ◽  
J. H. Kim
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Experiments ◽  
Mixed Finite Element ◽  
Mixed Finite Elements ◽  
Mixed Finite Element Method ◽  
Optimal Order ◽  
Order Convergence ◽  
New Family ◽  
Optimal Order Convergence

In this paper, we suggest a new patch condition for nonconforming mixed finite elements (MFEs) on parallelepiped and provide a framework for the convergence. Also, we introduce a new family of nonconforming MFE space satisfying the new patch condition. The numerical experiments show that the new MFE shows optimal order convergence in Hdiv and L2-norm for various problems with discontinuous coefficient case.

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.

ON THE CONVERGENCE OF A TRIANGULAR MIXED FINITE ELEMENT METHOD FOR REISSNER–MINDLIN PLATES

1996 ◽  
Vol 06 (03) ◽  
pp. 339-352 ◽  
Author(s):  
RICARDO G. DURÁN ◽  
ELSA LIBERMAN
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Experiments ◽  
Mixed Finite Element ◽  
Plate Thickness ◽  
Mixed Finite Element Method ◽  
Mindlin Plate ◽  
Optimal Order ◽  
The Difference ◽  
Element Method

We analyze the convergence of a mixed finite element method introduced by Zienkiewicz, Taylor, Papadopoulos and Oñate for the Reissner–Mindlin plate model. In order to do this, we compare it with a method which is known to be convergent with optimal order uniformly in the plate thickness. We show that the difference between the solutions of both methods is of higher order than the error. In particular the method does not present locking and is optimal order convergent. We also present several numerical experiments which confirm the similar behavior of both methods.

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