Adaptive finite element approximation of multiphysics problems

Larson, Mats G.; Bengzon, Fredrik

doi:10.1002/cnm.1087

Cited by 30 publications

(27 citation statements)

References 5 publications

(7 reference statements)

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“…The extension to the present situation of a two-step computation is rather straightforward, as is shown below; however, this extension is crucial for analyzing how discretization errors are carried over from one computation to the next in a sequential fashion. Goal-oriented a posteriori error estimates for estimating error transport between a sequence of direct problems, that is, without parameter identification have been developed in [9].…”

Section: Coupled System As a Special Case Of Identification Problemmentioning

confidence: 99%

Application-specific error control for parameter identification problems

Johansson

Larsson

Runesson

2011

Int. J. Numer. Meth. Biomed. Engng.

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SUMMARYAn often occurring scenario in the mathematical modeling of physical phenomena is that of a two-step computation consisting of, first, identifying a relevant parameter set from experiments (such as material parameters) and, second, carrying out a subsequent simulation using these parameters. In order to ensure the quality of the results from the simulation, the different sources of errors, for example, from discretization and inexact solution, must be traced and properly reduced. In this paper, a previously developed method for goal-oriented a posteriori error estimation for identification problems is extended to accommodate the combined identification and subsequent simulation.

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Section: Coupled System As a Special Case Of Identification Problemmentioning

confidence: 99%

Application-specific error control for parameter identification problems

Johansson

Larsson

Runesson

2011

Int. J. Numer. Meth. Biomed. Engng.

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“…Having selected the format of the quantity of interest given in (25) yields the adjoint problem (24) analogous to the original one (1). Thus, the same computer code available for solving the original problem (1) can be reused to solve the adjoint problem (26).…”

Section: The Estimation Of Value Lmentioning

confidence: 99%

“…Thus, an auxiliary problem, analogous to the adjoint problem (24), has to be introduced for the timeline quantity L O TL (·). This auxiliary problem is defined noting that, for a given time t ∈ I, the value s(t) = L …”

Section: Error Representation With Family Of Adjoint Problemsmentioning

confidence: 99%

“…For instance, quasi-steady-state non-linear problems are addressed in references [15,16,17,18], estimates for advection-diffusion-reaction equation are discussed in [19], similar approaches for the Stokes problem are presented in [20], and extension to parabolic time-dependent problems is introduced in [21,22,23]. Moreover, the same type of tools for coupled problems have been recently discussed in [24,25,26,27,28].…”

Section: Introductionmentioning

confidence: 99%

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Error Assessment in Structural Transient Dynamics

Verdugo

Mariné

Dı́ez

2014

Arch Computat Methods Eng

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This paper presents in a unified framework the most representative state-of-the-art techniques on a posteriori error assessment for second order hyperbolic problems, i.e., structural transient dynamics. For the sake of presentation, the error estimates are grouped in four types: recovery-based estimates, the dual weighted residual method, the constitutive relation error method and error estimates for timeline-dependent quantities of interest. All these methodologies give a comprehensive overview on the available error assessment techniques in structural dynamics, both for energy-like and goal-oriented estimates.

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“…These papers include research on aposteriori error estimation for boundary fluxes [1], general elements for fluid dynamics [2], mesh propagation patterns in certain local refinement schemes [3], fuzzy controllers in adaptivity [4], meshing deforming domains [5], multiscale algorithms [6], Sobolev gradient concepts for imaging [7], adaptivity for multiphysics problems [8] and coupled conduction-radiation problems [9].…”

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confidence: 99%

Editorial

Carey

Coutinho

2008

Commun. Numer. Meth. Engng.

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SUMMARYThis special issue contains papers from the 8th U.S. National Congress on Computational Mechanics (USNCCM), held in Austin, TX, U.S. A., 25-27 The U.S. national congresses in computational mechanics are a major forum for presenting a broad perspective of developments in methodology, algorithms, software and applications related to computational mechanics. These conferences meet over a period of approximately a week and involve numerous sessions running concurrently throughout the week. The sessions are diverse in nature and cover research on computational aspects of emerging applications, as well as more traditional areas such as computational fluid mechanics and computational solid mechanics. Sessions dealing with methodology, software and algorithms embrace such topics as uncertainty quantification, verification and validation, adaptive strategies, improved finite element methods, new stabilization techniques, and parallel simulation to name just a few. Following the USNCCM meeting in Austin 2005, contributions were selected for a special issue of CNME with a focus on novel methods and algorithms. These papers include research on aposteriori error estimation for boundary fluxes

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Adaptive finite element approximation of multiphysics problems

Cited by 30 publications

References 5 publications

Application-specific error control for parameter identification problems

Application-specific error control for parameter identification problems

Error Assessment in Structural Transient Dynamics

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