G1-Interpolation and geometry reconstruction for higher order finite elements

The paper proposes a new G1-interpolation and geometry reconstruction scheme for regular surfaces approximated with unstructured quadrilateral grids. The parametrization is based on C1 transfinite interpolation and sixth order polynomials. The G1-conforming approximation of surfaces guarantees continuity of surface normals and it is critical for higher order finite and boundary element discretizations on curvilinear domains. The proposed interpolation–reconstruction scheme is illustrated with a number of numerical examples including the geometry of human head.