A new variational self-regular traction-BEM formulation for inter-element continuity of displacement derivatives

In this work, a non-symmetric variational approach is derived to enforce C1,α continuity at inter-element nodes for the self-regular traction-BIE. This variational approach uses only Lagrangian C0 elements. Two separate algorithms are derived. The first one enforces C1,α continuity at smooth inter-element nodes, and the second enforces continuity of displacement derivatives in global coordinates at corner nodes, where C1,α continuity cannot be enforced. The variational formulation for the traction-BIE is implemented in this work for two elastostatics problems with various discretizations and polynomial interpolants. Local and global measures of the discretization error are obtained by means of an error estimator recently derived by the authors. Comparisons are also made with the displacement-BIE, which does not require C1,α continuity for the displacement. The lack of smoothness of the displacement derivatives at the inter-element nodes is shown to be an important source of both local and global error for the traction-BIE formulation, especially for quadratic elements. The accuracy of the boundary solution obtained from the traction-BIE improves significantly when C1,α continuity is enforced where possible, i.e., at the smooth inter-element nodes only.