Discontinuities are important in the mechanics of solids and fluids. Examples
are cracks, shear bands, rock faults, delamination and debonding. With mechanics
focusing on smaller and smaller length scales, e.g. on the description of phase
boundaries and dislocations, the need to properly model discontinuities
increases. While these examples pertain to solid mechanics, albeit at a wide
range of scales, technically important interface problems also appear at
fluid-solid boundaries, e.g. in welding and casting processes, and in
aeroelasticity.
Discretization methods have traditionally been developed for continuous media
and are less well suited for treating discontinuities. Indeed, they are
approximation methods for the solution of the partial differential equations,
which are