  Tectonic faults are commonly modelled as Volterra or Somigliana dislocations
in an elastic medium. Various solution methods exist for this problem. However,
the methods used in practice are often limiting, motivated by reasons of
computational efficiency rather than geophysical accuracy. A typical
geophysical application involves inverse problems for which many different
fault configurations need to be examined, each adding to the computational
load. In practice, this precludes conventional finite-element methods, which
suffer a large computational overhead on account of geometric changes. This
paper presents a new non-conforming finite-element method based on weak
imposition of the displacement discontinuity. The weak imposition of the
discontinuity enables the application of approximation spaces that are
independent of the dislocation geometry, thus enabling optimal reuse of
computational components. Such reuse of computational components renders
finite-element modeling a viable option for inverse problems in geophysical
applications. A detailed analysis of the approximation properties of the new
formulation is provided. The analysis is supported by numerical experiments in
2D and 3D.
