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The standard boundary node method (BNM) uses a (meshless) diffuse interpolation (in terms of neighbouring scattered boundary points) for the primary variables. The method is not ‘truly meshless’, however, since cells on the boundary of a body are used for integration. This paper presents a ‘pure’ version of the BNM in which integration cells are dispensed with. Instead (overlapping), regions of influence (ROIs) of boundary nodes are used for integration. Initial results for 2-D potential theory, presented here, are encouraging. Copyright © 2002 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The paper reveals the conditions under which the approximations of the normal vector and global coordinates of interior points of two segments on a smooth contour can fail using the C¹-continuous Overhauser elements. A new continuous modelling of the normal vector is developed using the standard Lagrange elements. The derivation is consistent with the assumptions employed in the boundary element method formulations of potential problems. Test numerical examples are considered in order to analyse the accuracy of the approximations based on the use of standard C0-continuous elements, Overhauser C1-continuous elements and the proposed 'smooth' C0 elements. [ABSTRACT FROM AUTHOR]