scholarly journals A Crank--Nicolson Finite Element Method and the Optimal Error Estimates for the Modified Time-Dependent Maxwell--Schrödinger Equations

2018 ◽  
Vol 56 (1) ◽  
pp. 369-396 ◽  
Author(s):  
Chupeng Ma ◽  
Liqun Cao
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Error Estimates ◽  
Time Dependent ◽  
Optimal Error Estimates ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Optimal Error ◽  
Element Method ◽  
Crank Nicolson

scholarly journals A Consistent Immersed Finite Element Method for the Interface Elasticity Problems

2016 ◽  
Vol 2016 ◽  
pp. 1-9
Author(s):  
Sangwon Jin ◽  
Do Y. Kwak ◽  
Daehyeon Kyeong
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Rates Of Convergence ◽  
Optimal Error Estimates ◽  
Optimal Error ◽  
Immersed Finite Element Method ◽  
Elasticity Problems ◽  
Interface Elasticity ◽  
Nonconforming Finite Element Methods ◽  
Element Method

We propose a new scheme for elasticity problems having discontinuity in the coefficients. In the previous work (Kwak et al., 2014), the authors suggested a method for solving such problems by finite element method using nonfitted grids. The proposed method is based on theP1-nonconforming finite element methods with stabilizing terms. In this work, we modify the method by adding the consistency terms, so that the estimates of consistency terms are not necessary. We show optimal error estimates inH1and divergence norms under minimal assumptions. Various numerical experiments also show optimal rates of convergence.

A Stabilized Finite Element Method for Non-Stationary Conduction-Convection Problems

2011 ◽  
Vol 3 (2) ◽  
pp. 239-258 ◽  
Author(s):  
Ke Zhao ◽  
Yinnian He ◽  
Tong Zhang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Optimal Error Estimates ◽  
Two Dimensional ◽  
Element Level ◽  
Optimal Error ◽  
Stabilized Finite Element ◽  
Stabilized Finite Element Method ◽  
The Stability ◽  
Element Method

AbstractThis paper is concerned with a stabilized finite element method based on two local Gauss integrations for the two-dimensional non-stationary conduction-convection equations by using the lowest equal-order pairs of finite elements. This method only offsets the discrete pressure space by the residual of the simple and symmetry term at element level in order to circumvent the inf-sup condition. The stability of the discrete scheme is derived under some regularity assumptions. Optimal error estimates are obtained by applying the standard Galerkin techniques. Finally, the numerical illustrations agree completely with the theoretical expectations.

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