Discontinuous Galerkin Finite Element Methods

The discontinuous Galerkin (DG, for short) method has been introduced in 1973 by Reed and Hill for the numerical approximation of hyperbolic problems. Also in the 1970s, DG methods for elliptic and parabolic equations were independently proposed and a number of variants introduced and studied. In recent years the DG methods have become increasingly popular. The reasons for this increase of interest are numerous, but essentially lie in the fact that allowing for discontinuities in the finite element approximation gives tremendous flexibility in terms of mesh design, choice of shape functions and development of hp-adaptive strategies. Indeed, DG methods naturally handle non-conforming meshes (possibly made of non-standard, arbitrarily-shaped elements) and elementwise varying polynomial approximation degrees.  Moreover, basic physical principles, such as conservation of mass, momentum and forces, can be naturally built into the method. Such a flexibility can be favorably exploited to deal with strong heterogeneity in the materials and/or complex geometries. The research at MOX  in this context, focuses on both the theoretical/computational approximation properties of DG methods as well as the application of DG methods to wide class of problems arising in various fields of Engineering.

View a list of journal publications and MOX Reports related to DG methods.

View a list of theses related to DG methods.

Discontinuous Galerkin Finite Element Methods

Spinodal decomposition. DG approximate solution of the Cahn-Hillard equation with degenerate mobility.