This paper considers a finite-element approximation of a Poisson equation in a region with a curved boundary on which a Neumann condition is prescribed. Piecewise linear and bilinear elements are used on unfitted meshes with the region of integration being replaced by a polygonal approximation. It is shown, despite the variational crimes, that the rate of convergence is still order (h) in the H1 norm. Numerical examples show that the method is easy to implement and that the predicted rate of convergence is obtained.
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Barrett et al. (1984) studied this question.
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