C1-continuous generalised parabolic blending elements in the Boundary Element Method

In the finite element and boundary element methods, one important source of error due to approximation arises from the form of the parametric representation used for defining the distribution of field functions over the domain and the topological positions of the domain geometry. In this paper, the standard C1-continuous Overhauser elements are modified to generalised parabolic blending (GPB) elements to make them adaptable to nonuniform meshing of the domain. These elements are applied to three-dimensional Boundary Element Method for potential problems and the results are compared with those of standard Overhauser elements. GPB elements ensure first derivative continuity where necessary and functional value continuity at all points, while they do not propagate local disturbances and do not require field derivatives at nodal points.