We generalize the technique of [Solving Dirichlet boundary-value problems oncurved domains by extensions from subdomains, SIAM J. Sci. Comput. 34, pp.A497--A519 (2012)] to elliptic problems with mixed boundary conditions andelliptic interface problems involving a non-polygonal interface. We study firstthe treatment of the Neumann boundary data since it is crucial to understandthe applicability of the technique to curved interfaces. We provide numericalresults showing that, in order to obtain optimal high order convergence, it isdesirable to construct the computational domain by interpolating theboundary/interface using piecewise linear segments. In this case the distanceof the computational domain to the exact boundary is only $O(h^2)$.
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机译：我们通过[SIAM J. Sci。]子域的扩展来概括[解决弯曲域上的Dirichlet边值问题。计算34，pp.A497--A519（2012）]涉及具有混合边界条件的椭圆问题和涉及非多边形界面的椭圆界面问题。我们首先研究Neumann边界数据的处理方法，因为了解该技术对弯曲界面的适用性至关重要。我们提供的数值结果表明，为了获得最佳的高阶收敛性，希望通过使用分段线性段对边界/接口进行插值来构造计算域。在这种情况下，计算域到精确边界的距离仅为$ O（h ^ 2）$。
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