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arXiv · 1610.04482

Fictitious domain method with boundary value correction using penalty-free Nitsche method

Thomas Boiveau·Erik Burman·Susanne Claus·Mats G. Larson
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Abstract

In this paper, we consider a fictitious domain approach based on a Nitsche type method without penalty. To allow for high order approximation using piecewise affine approximation of the geometry we use a boundary value correction technique based on Taylor expansion from the approximate to the physical boundary. To ensure stability of the method a ghost penalty stabilization is considered in the boundary zone. We prove optimal error estimates in the $H^1$-norm and estimates suboptimal by $\mathcal{O}(h^{\frac12})$ in the $L^2$-norm. The suboptimality is due to the lack of adjoint consistency of our formulation. Numerical results are provided to corroborate the theoretical study.

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Thomas Boiveau, Erik Burman, Susanne Claus, Mats G. Larson. 2016-10-14. Fictitious domain method with boundary value correction using penalty-free Nitsche method. https://arxiv.org/abs/1610.04482

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