Asymptotic Error Expansions for Stiff Equations: The Implicit Euler Scheme

1990 ◽  
Vol 27 (1) ◽  
pp. 67-104 ◽  
Author(s):  
W. Auzinger ◽  
R. Frank ◽  
F. Macsek
Keyword(s):  
Euler Scheme ◽  
Implicit Euler Scheme ◽  
Stiff Equations ◽  
Asymptotic Error ◽  
Asymptotic Error Expansions

Asymptotic error expansions for stiff equations: Applications

Computing ◽  
1990 ◽  
Vol 43 (3) ◽  
pp. 223-253 ◽  
Author(s):  
W. Auzinger ◽  
R. Frank ◽  
G. Kirlinger
Keyword(s):  
Stiff Equations ◽  
Asymptotic Error ◽  
Asymptotic Error Expansions

Time and space meshes adaptivity for the resolution of a semi-linear heat equation

2021 ◽  
pp. 1-10
Author(s):  
Nejmeddine Chorfi
Keyword(s):  
Parabolic Equation ◽  
Heat Equation ◽  
Order Of Convergence ◽  
Linear Parabolic Equation ◽  
Spectral Elements ◽  
Euler Scheme ◽  
Time Step ◽  
Implicit Euler Scheme ◽  
Linear Heat ◽  
Error Indicators

The aim of this work is to highlight that the adaptivity of the time step when combined with the adaptivity of the spectral mesh is optimal for a semi-linear parabolic equation discretized by an implicit Euler scheme in time and spectral elements method in space. The numerical results confirm the optimality of the order of convergence. The later is similar to the order of the error indicators.

Comparison of Two Time-Integration Algorithms for an Anisotropic Damage Model Coupled with Plasticity

2015 ◽  
Vol 784 ◽  
pp. 292-299 ◽  
Author(s):  
Stephan Wulfinghoff ◽  
Marek Fassin ◽  
Stefanie Reese
Keyword(s):  
Evolution Equations ◽  
Damage Model ◽  
Time Integration ◽  
Three Dimensional ◽  
Anisotropic Damage ◽  
Euler Scheme ◽  
The Finite Element Method ◽  
Time Step ◽  
Implicit Euler Scheme ◽  
Integration Algorithms

In this work, two time integration algorithms for the anisotropic damage model proposed by Lemaitre et al. (2000) are compared. Specifically, the standard implicit Euler scheme is compared to an algorithm which implicitly solves the elasto-plastic evolution equations and explicitly computes the damage update. To this end, a three dimensional bending example is solved using the finite element method and the results of the two algorithms are compared for different time step sizes.

Implicit Euler scheme for an abstract evolution inequality

2011 ◽  
Vol 47 (8) ◽  
pp. 1130-1138 ◽  
Author(s):  
R. Z. Dautov ◽  
A. I. Mikheeva
Keyword(s):  
Euler Scheme ◽  
Implicit Euler Scheme ◽  
Evolution Inequality

scholarly journals On the convergence of the wavelet-Galerkin method for nonlinear filtering

2010 ◽  
Vol 20 (1) ◽  
pp. 93-108 ◽  
Author(s):  
Łukasz Nowak ◽  
Monika Pasławska-Południak ◽  
Krystyna Twardowska
Keyword(s):  
Galerkin Method ◽  
Compact Support ◽  
Nonlinear Filtering ◽  
Euler Scheme ◽  
Zakai Equation ◽  
Implicit Euler Scheme ◽  
Galerkin Scheme ◽  
Wavelet Galerkin Method ◽  
Biorthogonal Basis ◽  
Filtering Problem

On the convergence of the wavelet-Galerkin method for nonlinear filteringThe aim of the paper is to examine the wavelet-Galerkin method for the solution of filtering equations. We use a wavelet biorthogonal basis with compact support for approximations of the solution. Then we compute the Zakai equation for our filtering problem and consider the implicit Euler scheme in time and the Galerkin scheme in space for the solution of the Zakai equation. We give theorems on convergence and its rate. The method is numerically much more efficient than the classical Galerkin method.

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