Conservative interpolation between volume meshes by local Galerkin projection

The problem of interpolating between discrete fields arises frequently in computational physics. The obvious approach, consistent interpolation, has several drawbacks such as suboptimality, non-conservation, and unsuitability for use with discontinuous discretisations. An alternative, Galerkin projection, remedies these deficiencies; however, its implementation has proven very challenging. This paper presents an algorithm for the local implementation of Galerkin projection of discrete fields between meshes. This algorithm extends naturally to three dimensions and is very efficient.