Dual weighted residual error estimation for the finite cell method

Stolfo, Paolo Di; Rademacher, Andreas; Schröder, Jörg

doi:10.1515/jnma-2017-0103

Cited by 20 publications

(23 citation statements)

References 37 publications

(50 reference statements)

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“…In this section, we present the results of two numerical examples from [5]. In the first one, the claim that the terms e N S,· in the error representation are negligibly small compared to the dominating error terms e D and e Q is validated.…”

Section: Numerical Resultsmentioning

confidence: 97%

“…by filtering, see [5] and references therein) Mark mesh elements with highest contributions, refine T , update and reduce by 1 on new mesh elements end if until termination criterion is met ∩ Ω is considered. by filtering, see [5] and references therein) Mark mesh elements with highest contributions, refine T , update and reduce by 1 on new mesh elements end if until termination criterion is met ∩ Ω is considered.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…The quadtree computation stops at approx. We refer to [5] where further numerical experiments are presented, in particular, in the context of model plasticity with linear isotropic hardining. While the adaptive refinement yields an optimal algebraic convergence of O(N −1 ), uniform refinement does not attain the optimal rate.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…The following error representation is derived in [5] and contains the evaluation of the approximated operators as well as the exact operators. The evaluation of the latter involves integrals on Ω which cannot be calculated exactly.…”

Section: A Posteriori Error Controlmentioning

confidence: 99%

“…The focus is on the application of the dual weighted residual approach (DWR) as presented in [5]. The focus is on the application of the dual weighted residual approach (DWR) as presented in [5].…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

A posteriori error control for the finite cell method

Stolfo

Düster

Kollmannsberger

et al. 2019

Proc Appl Math and Mech

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The paper presents some concepts of the finite cell method and discusses a posteriori error control for this approach. The focus is on the application of the dual weighted residual approach (DWR), which enables the control of the error with respect to a user-defined quantity of interest. Since both the discretization error and the quadrature error are estimated, the application of the DWR approach provides an adaptive strategy which equilibrates the error contributions resulting from discretization and quadrature. The strategy consists in refining either the finite cell mesh or its associated quadrature mesh. Numerical experiments confirm the performance of the error control and the adaptive scheme for a non-linear problem in 2D.

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Section: Numerical Resultsmentioning

confidence: 97%

Section: Numerical Resultsmentioning

confidence: 99%

Section: Numerical Resultsmentioning

confidence: 99%

Section: A Posteriori Error Controlmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

A posteriori error control for the finite cell method

Stolfo

Düster

Kollmannsberger

et al. 2019

Proc Appl Math and Mech

Self Cite

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From image data towards microstructure information – Accuracy analysis at the digital core of materials

2020

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A cornerstone of computational solid mechanics in the context of digital transformation are databases for microstructures obtained from advanced tomography techniques. Uniform discretizations of pixelized images in 2D are the raw‐data point of departure for simulation analyses. This paper proposes the concept of a unified error analysis for image‐based microstructure representations in uniform resolution along with adaptively coarsened discretizations. The analysis distinguishes between a resolution error due to finite, possibly coarsened image resolution and a discretization error, and investigates their quantitative relation, spatial distributions and their impacts on the simulation results both on the microscale and the macroscale in the context of computational homogenization. The assessment of accuracy and efficiency is carried out for an exemplary two‐phase material. Beyond the example considered here the concept is a rational tool in the transformation of raw image data into microstructure information adapted to particular simulation needs and endows the digital twin of real microstructures with validated characteristics for reliable, predictive simulations.

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