This paper examines different mesh boundary curving algorithms in the particular case where no exact geometric description is available. The starting point for the curving is typically a coarse linear mesh, whereas the target geometry is represented by a refined linear mesh. Both can be generated using a classical linear mesh generator. Two different boundary curving algorithms are examined. The first algorithm is based on Lagrange nodal high-order polynomial interpolation where the interpolation nodes are iteratively moved towards the target curve. Relocation steps are included in each iteration to approximately preserve the original node spacing. The second algorithm is based on hierarchic modal shape functions. In a reference frame, projection based interpolation is applied that minimizes the distance between the interpolating function and the local target function in the H-seminorm. The performance and accuracy of the two methods are evaluated and compared. Thereby, the area between the target and the approximating curve is used as error measure. In general, both methods exhibit similar levels of performance. A lower bound on the accuracy is observed that depends on the level of refinement of the target mesh. Differences lie in the applicability of the two methods. For the method based on modal interpolation, several initial requirements have to be fulfilled. The method based on nodal interpolation on the other hand is simpler but less robust. Overall, the modal interpolation approach is preferable, where applicable.
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