scholarly journals A local error estimate of the method of multi-scale asymptotic expansions for elliptic problems with rapidly oscillatory coefficients

2007 ◽  
Vol 329 (1) ◽  
pp. 547-556 ◽  
Author(s):  
Wen-ming He ◽  
Jun-zhi Cui
Keyword(s):  
Error Estimate ◽  
Asymptotic Expansions ◽  
Elliptic Problems ◽  
Local Error ◽  
Multi Scale ◽  
Local Error Estimate

Kriging regression of PIV data using a local error estimate

2014 ◽  
Vol 55 (1) ◽  
Author(s):  
Jouke H. S. de Baar ◽  
Mustafa Percin ◽  
Richard P. Dwight ◽  
Bas W. van Oudheusden ◽  
Hester Bijl
Keyword(s):  
Error Estimate ◽  
Local Error ◽  
Local Error Estimate

scholarly journals A Multi-Scale Model of Soft Imperfect Interface with Nonlocal Damage

2019 ◽  
Vol 10 (01) ◽  
pp. 1841001
Author(s):  
Asghar Ali Maitlo ◽  
Frédéric Lebon ◽  
Caroline Bauzet
Keyword(s):  
Asymptotic Expansions ◽  
Composite Structure ◽  
Imperfect Interface ◽  
Unilateral Constraint ◽  
Microscopic Level ◽  
Scale Model ◽  
Nonlocal Damage ◽  
Multi Scale ◽  
Bonded Interface ◽  
Unilateral Conditions

The aim of this paper is to propose a model of bonded interface including nonlocal damage and unilateral conditions. The model is derived from the problem of a composite structure made by two adherents and a thin adhesive. The adhesive is damaged at microscopic level and is subjected to two regimes, one in traction and one in compression. The model of interface is derived by matched asymptotic expansions. In this paper, two cases corresponding to the two regimes are discussed. Moreover, this model can be considered as a model of contact with adhesion and unilateral constraint. At the end of the paper, a simple numerical example is presented to show the evolution of the model.

A Survey in Mathematics for Industry: Two-timing and matched asymptotic expansions for singular perturbation problems

2011 ◽  
Vol 22 (6) ◽  
pp. 613-629 ◽  
Author(s):  
R. E. O'MALLEY ◽  
E. KIRKINIS
Keyword(s):  
Asymptotic Expansions ◽  
Multiple Scale ◽  
Singularly Perturbed ◽  
Matched Asymptotic Expansions ◽  
Amplitude Equations ◽  
Singularly Perturbed Problems ◽  
Multi Scale ◽  
Scale Method ◽  
Perturbation Problems ◽  
Appl Math

Following the derivation of amplitude equations through a new two-time-scale method [O'Malley, R. E., Jr. & Kirkinis, E (2010) A combined renormalization group-multiple scale method for singularly perturbed problems.Stud. Appl. Math.124, 383–410], we show that a multi-scale method may often be preferable for solving singularly perturbed problems than the method of matched asymptotic expansions. We illustrate this approach with 10 singularly perturbed ordinary and partial differential equations.

scholarly journals Goal Oriented Time Adaptivity Using Local Error Estimates

Algorithms ◽  
2020 ◽  
Vol 13 (5) ◽  
pp. 113
Author(s):  
Peter Meisrimel ◽  
Philipp Birken
Keyword(s):  
Error Estimates ◽  
Initial Value Problems ◽  
Error Propagation ◽  
Adaptive Methods ◽  
Local Error ◽  
A Posteriori ◽  
Initial Value ◽  
Numerical Tests ◽  
Performance Predictions ◽  
Local Error Estimate

We consider initial value problems (IVPs) where we are interested in a quantity of interest (QoI) that is the integral in time of a functional of the solution. For these, we analyze goal oriented time adaptive methods that use only local error estimates. A local error estimate and timestep controller for step-wise contributions to the QoI are derived. We prove convergence of the error in the QoI for tolerance to zero under a controllability assumption. By analyzing global error propagation with respect to the QoI, we can identify possible issues and make performance predictions. Numerical tests verify these results. We compare performance with classical local error based time-adaptivity and a posteriori based adaptivity using the dual-weighted residual (DWR) method. For dissipative problems, local error based methods show better performance than DWR and the goal oriented method shows good results in most examples, with significant speedups in some cases.

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