Mesh generation over curved surfaces with explicit control on discretization error

A scheme is presented for the automatic generation of triangular meshes over general analytical curved surfaces with explicit control on the discretization error over the interior of the domain. The element size on the curved surface is estimated based on the given allowable discretization error and the surface curvature. The mesh generation starts with the subdivision of the curved boundary of the domain into straight line segments in compliance with the given discretization error constraint. Elements are generated directly over the surface in such a way that the discretization error is kept within the required geometrical tolerance. Those elements violating the given constraint are noted and post‐processed by either element subdivision or node repositioning. Various schemes as to how improvement should be made are proposed, which reduce the discretization error by different strategies depending on the position of the point where the maximum discretization error occurs.