The variational bi-complex formulation of Maxwell’s equations

Solving Maxwell's equations using the ultra weak variational formulation

We investigate the ultra weak variational formulation for simulating time-harmonic Maxwell problems. This study has two main goals. First, we introduce a novel derivation of the UWVF method which shows that the UWVF is an unusual version of the standard upwind discontinuous Galerkin (DG) method with a special choice of basis functions. Second, we discuss the practical implementation of an elect...

Variational Formulation for the Kpz and Related Kinetic Equations

We present a variational formulation for the Kardar-Parisi-Zhang (KPZ) equation that leads to a thermodynamic-like potential for the KPZ as well as for other related kinetic equations. For the KPZ case, with the knowledge of such a potential we prove some global shift invariance properties previously conjectured by other authors. We also show a few results about the form of the stationary proba...

A Variational Complex for Difference Equations

Extended Variational Formulation for Heterogeneous Partial Differential Equations

We address the coupling of an advection equation with a diffusion-advection equation, for solutions featuring boundary layers. We consider non-overlapping domain decompositions and we face up the heterogeneous problem using an extended variational formulation. We will prove the equivalence between the latter formulation and a treatment based on a singular perturbation theory. An exhaustive comp...

Variational Formulation of Problems and Variational Methods