On the error behaviour of force andmoment sources in tetrahedral spectral finite elements

The representation of a force or of a moment point source in a spectral finite-element code for modelling elastic wave propagation becomes fundamentally different in degenerate cases where the source is located on the boundary of an element. This difference is related to the fact that the finite-element basis functions are continuous across element boundaries, but their derivatives are not. A method is presented that effectively deals with this problem. Tests on 1-D elements show that the numerical errors for a force source follow the expected convergence rate in terms of the element size, apart from isolated cases where superconvergence occurs. For a moment source, the method also converges but one order of accuracy is lost, probably because of the reduced regularity of the problem. Numerical tests in 3D on continuous mass-lumped tetrahedral elements show a similar error behaviour as in the 1-D case, although in 3D, the loss of accuracy for the moment source is not a severe as a full order.