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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.

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