A posteriori error analysis of multiscale operator decomposition methods for multiphysics models

Estep, D.; Carey, Varis; Ginting, Victor; Tavener, Simon; Wildey, Timothy Michael

doi:10.1088/1742-6596/125/1/012075

Cited by 15 publications

(12 citation statements)

References 16 publications

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“…In [3] these results are extended to heat transfer in time-dependent incompressible flow. Closely related results are presented by Estep and coworkers [4] in the context of multiscale operator decomposition for elliptic problems. In [5] Gräetsch and Bathe propose a duality-based error estimation technique for fully coupled fluid-structure interaction problems.…”

Section: Introductionmentioning

confidence: 61%

Adaptive finite element approximation of multiphysics problems: A fluid–structure interaction model problem

Bengzon

Larson

2010

Numerical Meth Engineering

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SUMMARYIn this paper we consider finite element simulation of the mechanical response of an elastic solid immersed into a viscous incompressible fluid flow. For simplicity, we assume that the mechanics of the solid is governed by linear elasticity and the motion of the fluid by the Stokes equation. For this one-way coupled multiphysics problem we derive an a posteriori error estimate using duality techniques. Based on the estimate we propose an adaptive algorithm that automatically constructs a suitable mesh for the fluid and solid computational domains given a specific goal quantity for the elastic problem.

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Section: Introductionmentioning

confidence: 61%

Adaptive finite element approximation of multiphysics problems: A fluid–structure interaction model problem

Bengzon

Larson

2010

Numerical Meth Engineering

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“…Our development of the a posteriori error analysis is demonstrated in the context of convection-diffusion-reaction systems. IMEX approaches raise additional reasons for quantitative error estimation, since IMEX methods fall in the general category of operator decomposition/finite iteration methods [18,[26][27][28][29][30], and thus give rise to additional sources of instability and discretization errors compared to fully implicit methods. Further, error estimates are required to construct adaptive algorithms and this is an active area of current research (see e.g.…”

Section: Introductionmentioning

confidence: 99%

A posteriori error analysis of IMEX multi-step time integration methods for advection–diffusion–reaction equations

Chaudhry

Estep

Ginting

et al. 2015

Computer Methods in Applied Mechanics and Engineering

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Implicit-Explicit (IMEX) schemes are an important and widely used class of time integration methods for both parabolic and hyperbolic partial differential equations. We develop accurate a posteriori error estimates for a user-defined quantity of interest for two classes of multi-step IMEX schemes for advection-diffusion-reaction problems. The analysis proceeds by recasting the IMEX schemes into a variational form suitable for a posteriori error analysis employing adjoint problems and computable residuals. The a posteriori estimates quantify distinct contributions from various aspects of the spatial and temporal discretizations, and can be used to evaluate discretization choices. Numerical results are presented that demonstrate the accuracy of the estimates for a representative set of problems. Published by Elsevier B.V.

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“…Accurate estimation of local QoIs can be achieved using goal-oriented error estimation and adaptive techniques based on the use of adjoint methods [4,5]. Adjoint methods can also be used to improve the computational performance of parameter http://www.amses-journal.com/content/2/1/15 sensitivity analyses [6], especially for systems with a large number of parameters.…”

Section: Introductionmentioning

confidence: 99%

Adjoint-consistent formulations of slip models for coupled electroosmotic flow systems

Garg

Prudhomme

Zee

et al. 2014

Adv. Model. and Simul. in Eng. Sci.

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Background: Models based on the Helmholtz 'slip' approximation are often used for the simulation of electroosmotic flows. The objectives of this paper are to construct adjoint-consistent formulations of such models, and to develop adjoint-based numerical tools for adaptive mesh refinement and parameter sensitivity analysis. Methods: We show that the direct formulation of the 'slip' model is adjoint inconsistent, and leads to an ill-posed adjoint problem. We propose a modified formulation of the coupled 'slip' model, which is shown to be well-posed, and therefore automatically adjoint-consistent. Results: Numerical examples are presented to illustrate the computation and use of the adjoint solution in two-dimensional microfluidics problems. Conclusions: An adjoint-consistent formulation for Helmholtz 'slip' models of electroosmotic flows has been proposed. This formulation provides adjoint solutions that can be reliably used for mesh refinement and sensitivity analysis.

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A posteriori error analysis of multiscale operator decomposition methods for multiphysics models

Cited by 15 publications

References 16 publications

Adaptive finite element approximation of multiphysics problems: A fluid–structure interaction model problem

Adaptive finite element approximation of multiphysics problems: A fluid–structure interaction model problem

A posteriori error analysis of IMEX multi-step time integration methods for advection–diffusion–reaction equations

Adjoint-consistent formulations of slip models for coupled electroosmotic flow systems

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