Weifeng Qiu, Manuel Solano:
High order approximation of mixed boundary value problems in curved domains by extensions from polygonal subdomains
This paper is a continuation of [Solving Dirichlet boundary-value problems on curved domains by extensions from subdomains, SIAM J. Sci. Comput. 34, pp. A497-A519 (2012)]. We generalize this technique of high order approximation of boundary value problems in curved domains with Dirichlet boundary data to the case of mixed boundary conditions. The treatment to Neumann boundary data is novel. We provide numerical results showing that, in order to obtain optimal high order convergence in this generalized setting, it is desirable to construct the computational domain by interpolating the boundary using piecewise linear segment. In this case the distance from the computational domain to the exact boundary is only O(h²).