In this paper, we consider a fictitious domain approach based on a Nitschetype method without penalty. To allow for high order approximation usingpiecewise affine approximation of the geometry we use a boundary valuecorrection technique based on Taylor expansion from the approximate to thephysical boundary. To ensure stability of the method a ghost penaltystabilization is considered in the boundary zone. We prove optimal errorestimates in the $H^1$-norm and estimates suboptimal by$\mathcal{O}(h^{\frac12})$ in the $L^2$-norm. The suboptimality is due to thelack of adjoint consistency of our formulation. Numerical results are providedto corroborate the theoretical study.
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机译：在本文中，我们考虑一种基于Nitschetype方法的虚拟域方法，而不会产生任何惩罚。为了允许使用几何的逐段仿射近似进行高阶近似，我们使用了基于从近似边界到物理边界的泰勒展开的边界值校正技术。为了确保该方法的稳定性，在边界区域考虑了重影稳定化。我们证明了在$ H ^ 1 $范数中的最优误差估计，并在$ L ^ 2 $范数中以$ \ mathcal {O}（h ^ {\ frac12}）$次优。亚最优性是由于我们的配方缺乏伴随的一致性。提供数值结果以证实理论研究。
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