scholarly journals An Optimal Error Estimates of Rothe-Finite element method for Nonlocal evolution equation

2021 ◽  
Author(s):  
Manal Djaghout
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Evolution Equation ◽  
Error Estimates ◽  
Optimal Error Estimates ◽  
Optimal Error ◽  
Nonlocal Evolution Equation ◽  
Element Method

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.

scholarly journals L ∞-error estimates of a finite element method for Hamilton-Jacobi-Bellman equations with nonlinear source terms with mixed boundary condition

2021 ◽  
Vol 54 (1) ◽  
pp. 452-461
Author(s):  
Madjda Miloudi ◽  
Samira Saadi ◽  
Mohamed Haiour
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Error Estimates ◽  
Mixed Boundary ◽  
Optimal Error Estimates ◽  
Source Terms ◽  
Nonlinear Source ◽  
Bellman Equations ◽  
Hamilton Jacobi Bellman ◽  
Element Method

Abstract In this paper, we introduce a new method to analyze the convergence of the standard finite element method for Hamilton-Jacobi-Bellman equation with noncoercive operators with nonlinear source terms with the mixed boundary conditions. The method consists of combining Bensoussan-Lions algorithm with the characterization of the solution, in both the continuous and discrete contexts, as fixed point of contraction. Optimal error estimates are then derived, first between the continuous algorithm and its finite element counterpart and then between the continuous solution and the approximate solution.

A Numerical Analysis of the Weak Galerkin Method for the Helmholtz Equation with High Wave Number

2017 ◽  
Vol 22 (1) ◽  
pp. 133-156 ◽  
Author(s):  
Yu Du ◽  
Zhimin Zhang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Error Estimates ◽  
Phase Error ◽  
Three Dimensions ◽  
Wave Number ◽  
Weak Galerkin ◽  
High Wave Number ◽  
Large Wave ◽  
Element Method

AbstractWe study the error analysis of the weak Galerkin finite element method in [24, 38] (WG-FEM) for the Helmholtz problem with large wave number in two and three dimensions. Using a modified duality argument proposed by Zhu and Wu, we obtain the pre-asymptotic error estimates of the WG-FEM. In particular, the error estimates with explicit dependence on the wave numberkare derived. This shows that the pollution error in the brokenH1-norm is bounded byunder mesh conditionk7/2h2≤C0or (kh)2+k(kh)p+1≤C0, which coincides with the phase error of the finite element method obtained by existent dispersion analyses. Herehis the mesh size,pis the order of the approximation space andC0is a constant independent ofkandh. Furthermore, numerical tests are provided to verify the theoretical findings and to illustrate the great capability of the WG-FEM in reducing the pollution effect.

Sign in / Sign up

Export Citation Format

Share Document