# Correction to: Enhanced numerical integration scheme based on image-compression techniques: application to fictitious domain methods

The Original Article was published on 06 May 2020

## Correction to: Adv. Model. and Simul. in Eng. Sci. (2020) 7:21 https://doi.org/10.1186/s40323-020-00157-2

Following publication of the original article [1], the authors reported the errors in the equation and in the text.

The corrected text and equation are given below:

First, we evaluate the quality and reliability of the results obtained when using the three methods investigated in this section. In Fig. 22, the errors in the energy norm

\begin{aligned} ||e||_{{\mathrm {E}}(\Omega _{\mathrm {e}})} = \sqrt{\left| \dfrac{{\mathcal {B}}(\textit{\textbf{u}}_{\mathrm {ref}}, \textit{\textbf{u}}_{\mathrm {ref}})-{\mathcal {B}}(\textit{\textbf{u}}, \textit{\textbf{u}})}{{\mathcal {B}}(\textit{\textbf{u}}_{\mathrm {ref}}, \textit{\textbf{u}}_{\mathrm {ref}})} \right| } \cdot 100 [\%], \end{aligned}
(20)

for various input parameters are presented, which should be minimized by the FCM solution on the energy space$$E(\Omega _{\mathrm {e}})$$ over the domain $$\Omega _{\mathrm {e}}$$ [3, 33]. In Eq. (20), $$\textit{\textbf{u}}$$ is the displacement field obtained by the FCM solution and $$\textit{\textbf{u}}_{\mathrm {ref}}$$ is the reference solution, obtained by p-FEM using blending functions [113] for an exact geometry mapping, resulting in a strain energy of $$1/2 \cdot {\mathcal {B}}(\textit{\textbf{u}}_{\mathrm {ref}},\textit{\textbf{u}}_{\mathrm {ref}}) = 0.7021812127$$ [31]. Besides investigating the global quality of the results based on $$||e||_{{\mathrm {E}}(\Omega _{\mathrm {e}})}$$, we also evaluate the solution based on point-wise values of the stress-fields $$\sigma _{\mathrm {vM}}$$ and $$\sigma _{\mathrm {yy}}$$ along the diagonal $$\overline{AB}$$ in Fig. 21, where $$\sigma _{\mathrm {vM}}$$ is the von Mises stress and $$\sigma _{\mathrm {yy}}$$ the stress in the y-direction.

The original article [1] has been updated.

## Reference

1. Márton P, Fabian D, Sascha E. Enhanced numerical integration scheme based on image-compression techniques: application to fictitious domain methods. Adv Model Simul Eng Sci. 2020;7:21.

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Correspondence to Márton Petö.

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